Pub Date : 1900-01-01DOI: 10.3318/PRIA.2002.102.2.205
A. Smoktunowicz
{"title":"Amitsur's Conjecture on Polynomial Rings in N Commuting Indeterminates","authors":"A. Smoktunowicz","doi":"10.3318/PRIA.2002.102.2.205","DOIUrl":"https://doi.org/10.3318/PRIA.2002.102.2.205","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134189582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2008.108.1.65
F. Catino, S. Siciliano, Ernesto Spinelli
It is well known that a modular group algebra KG is Lie nilpotent if, and only if, its unit group U(KG) is nilpotent. In this note we prove that if G is a torsion group, then the equality cIl(KG) = c'(U(KG)) occurs.
{"title":"A NOTE ON THE NILPOTENCY CLASS OF THE UNIT GROUP OF A MODULAR GROUP ALGEBRA","authors":"F. Catino, S. Siciliano, Ernesto Spinelli","doi":"10.3318/PRIA.2008.108.1.65","DOIUrl":"https://doi.org/10.3318/PRIA.2008.108.1.65","url":null,"abstract":"It is well known that a modular group algebra KG is Lie nilpotent if, and only if, its unit group U(KG) is nilpotent. In this note we prove that if G is a torsion group, then the equality cIl(KG) = c'(U(KG)) occurs.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133076295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"UNIVERSAL N-TUPLES OF OPERATORS","authors":"V. Müller","doi":"10.1353/mpr.2013.0015","DOIUrl":"https://doi.org/10.1353/mpr.2013.0015","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133519460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2005.105.1.93
Miroslav Kureš
The canonical involution in the second order iterated tangent bundle is generalised for an arbitrary order and transfered to jet spaces. The classification of all symmetrised nonholonomic jets of the third order is given.
将二阶迭代切束中的正则对合推广到任意阶，并将其推广到射流空间。给出了所有三阶对称非完整射流的分类。
{"title":"ON THE SYMMETRISATION OF NONHOLONOMIC JETS","authors":"Miroslav Kureš","doi":"10.3318/PRIA.2005.105.1.93","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.1.93","url":null,"abstract":"The canonical involution in the second order iterated tangent bundle is generalised for an arbitrary order and transfered to jet spaces. The classification of all symmetrised nonholonomic jets of the third order is given.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132671603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2005.105.2.25
A. Kiselev
A non-self-adjoint, rank-one Friedrichs model operator in L2(R) is considered in the case where the determinant of perturbation is an outer function in the half-planes C§. Its spectral structure is investigated. The impact of the linear resolvent growth condition on its spectral properties (including the similarity problem) is studied.
{"title":"SOME SPECTRAL PROPERTIES OF THE NON-SELF-ADJOINT FRIEDRICHS MODEL OPERATOR","authors":"A. Kiselev","doi":"10.3318/PRIA.2005.105.2.25","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.2.25","url":null,"abstract":"A non-self-adjoint, rank-one Friedrichs model operator in L2(R) is considered in the case where the determinant of perturbation is an outer function in the half-planes C§. Its spectral structure is investigated. The impact of the linear resolvent growth condition on its spectral properties (including the similarity problem) is studied.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133124522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/pria.2013.113.07
R. Harte, F. Holland, L. Mittenthal, R. Smyth, R. Timoney
The Trevor West I knew was called Tim, and he stayed that way for the first two years of our acquaintance, until his brother John arrived to set the record straight. He and I stayed yoked together through four years in Trinity and three more in Cambridge. We started off on an uneasy footing: Trevor had been expected to take the First Entrance Scholarship in Mathematics in 1956, and I, brash Northerner, came steaming down on the Enterprise and snatched it from under his nose. I went on to compound the offence by sitting the Foundation Scholarship in the same year: thanks to the innocence of Ludwig Bass, who set a Mechanics paper that completely floored the Senior Freshmen, I walked away with it. The following year, however, while Trevor and the rest of the class attended Schol classes, I was clearly above that sort of thing now. Of course Schol and Mod Part I were essentially the same, and I got my come-uppance the following September when Trevor scored a healthy First while I stumbled home with a II. 2. The year after we were a class of three: Trevor, myself and Michael Robinson, brother-in-law of President Mary. One year later, and the looming threat of fellow student John J. Miller brought Trevor round to combine efforts with me to keep him at bay. Trevor was always very savvy: when he told me afterwards T.S. Broderick approached him in Front Square to ask, 'What shall we do about Harte', he was quick to reply, 'If he's going to Cambridge he's going to need a First'. Savvy as ever, when we set out for Cambridge, Trevor was determined that we should on no account allow the Brits to see the depths of our ignorance. It was true that several recent Trinity exports to Cambridge had faltered: John Killen had been taken ill in his Moderatorship exam and been awarded a temporary Pass degree, historian Stephen Barcroft, who had elected to take his degree by thesis had had it rejected, and then P.A. Olagunju had died in Nigeria while rewriting his Cambridge dissertation.
我认识的特雷弗·韦斯特叫蒂姆，在我们认识的头两年里，他一直叫这个名字，直到他的哥哥约翰来纠正了这个错误。我和他一起在三一学院待了四年，在剑桥又待了三年。我们的起点并不稳:特雷弗本来有望在1956年获得数学第一入学奖学金，而我，一个傲慢的北方人，冲到进取号上，从他的鼻子底下抢走了奖学金。我在同一年参加了基金会奖学金的考试，这让我更受冒犯:多亏了路德维希·巴斯(Ludwig Bass)的清白，他在力学方面的考卷把高年级新生们彻底难倒了，我才拿到了奖学金。然而，第二年，当特雷弗和班上其他同学去学校上课的时候，我显然已经不关心这种事了。当然，学校和Mod第一部分基本上是一样的，我得到了我的报应，在接下来的9月，特雷弗得到了一个健康的第一，而我却跌跌撞撞地拿了一个第二。2. 第二年，我们变成了一个三人班:特雷弗、我和迈克尔·罗宾逊，玛丽校长的姐夫。一年后，同学约翰·j·米勒(John J. Miller)的威胁迫在眉睫，特雷弗决定和我一起努力阻止他。特雷弗总是很精明:事后他告诉我，T.S.布罗德里克在前广场找到他，问他:“我们该拿哈特怎么办?”他很快回答说:“如果他要去剑桥，他就需要一个First。”一如既往的精明，当我们出发去剑桥时，特雷弗下定决心绝不能让英国人看到我们的无知有多深。的确，三一学院最近几次向剑桥大学的出口都受到了影响:约翰·基伦在主持考试中生病，被授予临时及格学位;历史学家斯蒂芬·巴克罗夫特选择以论文方式获得学位，但被拒绝了;然后P.A.奥拉贡朱在重写剑桥大学的论文时在尼日利亚去世。
{"title":"SOME RECOLLECTIONS OF TREVOR WEST MRIA","authors":"R. Harte, F. Holland, L. Mittenthal, R. Smyth, R. Timoney","doi":"10.3318/pria.2013.113.07","DOIUrl":"https://doi.org/10.3318/pria.2013.113.07","url":null,"abstract":"The Trevor West I knew was called Tim, and he stayed that way for the first two years of our acquaintance, until his brother John arrived to set the record straight. He and I stayed yoked together through four years in Trinity and three more in Cambridge. We started off on an uneasy footing: Trevor had been expected to take the First Entrance Scholarship in Mathematics in 1956, and I, brash Northerner, came steaming down on the Enterprise and snatched it from under his nose. I went on to compound the offence by sitting the Foundation Scholarship in the same year: thanks to the innocence of Ludwig Bass, who set a Mechanics paper that completely floored the Senior Freshmen, I walked away with it. The following year, however, while Trevor and the rest of the class attended Schol classes, I was clearly above that sort of thing now. Of course Schol and Mod Part I were essentially the same, and I got my come-uppance the following September when Trevor scored a healthy First while I stumbled home with a II. 2. The year after we were a class of three: Trevor, myself and Michael Robinson, brother-in-law of President Mary. One year later, and the looming threat of fellow student John J. Miller brought Trevor round to combine efforts with me to keep him at bay. Trevor was always very savvy: when he told me afterwards T.S. Broderick approached him in Front Square to ask, 'What shall we do about Harte', he was quick to reply, 'If he's going to Cambridge he's going to need a First'. Savvy as ever, when we set out for Cambridge, Trevor was determined that we should on no account allow the Brits to see the depths of our ignorance. It was true that several recent Trinity exports to Cambridge had faltered: John Killen had been taken ill in his Moderatorship exam and been awarded a temporary Pass degree, historian Stephen Barcroft, who had elected to take his degree by thesis had had it rejected, and then P.A. Olagunju had died in Nigeria while rewriting his Cambridge dissertation.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114463490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2004.104.1.59
C. Meehan
We consider endomorphisms of M, a free R-module of arbitrary rank, where R is an associative unital ring with the property that every element of R is a sum of two units of R. We prove that every endomorphism of M is a sum of two automorphisms of M.
{"title":"SUMS OF AUTOMORPHISMS OF FREE ABELIAN GROUPS AND MODULES","authors":"C. Meehan","doi":"10.3318/PRIA.2004.104.1.59","DOIUrl":"https://doi.org/10.3318/PRIA.2004.104.1.59","url":null,"abstract":"We consider endomorphisms of M, a free R-module of arbitrary rank, where R is an associative unital ring with the property that every element of R is a sum of two units of R. We prove that every endomorphism of M is a sum of two automorphisms of M.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116430564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2005.105.2.1
R. Brits, L. Lindeboom, H. Raubenheimer
We characterise ideals consisting of generalised invertible elements in a semisimple Banach algebra.
我们刻画了半简单巴拿赫代数中由广义可逆元组成的理想。
{"title":"ON IDEALS OF GENERALISED INVERTIBLE ELEMENTS IN BANACH ALGEBRAS","authors":"R. Brits, L. Lindeboom, H. Raubenheimer","doi":"10.3318/PRIA.2005.105.2.1","DOIUrl":"https://doi.org/10.3318/PRIA.2005.105.2.1","url":null,"abstract":"We characterise ideals consisting of generalised invertible elements in a semisimple Banach algebra.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123393450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/pria.2018.118.07
R. Harte
{"title":"Spectral Disjointness and the Euclidean Algorithm","authors":"R. Harte","doi":"10.3318/pria.2018.118.07","DOIUrl":"https://doi.org/10.3318/pria.2018.118.07","url":null,"abstract":"","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124828870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.3318/PRIA.2010.110.1.73
M. Berkani, H. Zariouh
In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.
{"title":"EXTENDED WEYL TYPE THEOREMS AND PERTURBATIONS","authors":"M. Berkani, H. Zariouh","doi":"10.3318/PRIA.2010.110.1.73","DOIUrl":"https://doi.org/10.3318/PRIA.2010.110.1.73","url":null,"abstract":"In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128538672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：