Pub Date : 2019-05-16DOI: 10.1201/9780429187605-10
K. Benabdallah, A. Mader
{"title":"Greatest Common Divisors Generalized","authors":"K. Benabdallah, A. Mader","doi":"10.1201/9780429187605-10","DOIUrl":"https://doi.org/10.1201/9780429187605-10","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"54 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121538354","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 : 2019-05-16DOI: 10.1201/9780429187605-26
Saad H. Mohamed, Bruno J. Müller
{"title":"ℵ-Exchange Rings","authors":"Saad H. Mohamed, Bruno J. Müller","doi":"10.1201/9780429187605-26","DOIUrl":"https://doi.org/10.1201/9780429187605-26","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"195 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122518450","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 : 2019-05-16DOI: 10.1201/9780429187605-37
R. Wisbauer
Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples of (not self-small) tilting modules are I Q/ZZ in the category of torsion ZZ-modules, I Q⊕ I Q/ZZ in the category ZZ-Mod, certain divisible modules over integral domains, and also cohereditary coalgebras C over a QF-ring in the category of comodules over C. Self-small tilting modules P in σ[M ] are finitely presented in σ[M ]. For M = P , they are just the ∗-modules introduced by C. Menini and A. Orsatti, and for M = R, they are the usual tilting modules considered in representation theory. Notice that our techniques and most of our results also apply to locally finitely generated Grothendieck categories.
{"title":"Tilting in Module Categories","authors":"R. Wisbauer","doi":"10.1201/9780429187605-37","DOIUrl":"https://doi.org/10.1201/9780429187605-37","url":null,"abstract":"Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples of (not self-small) tilting modules are I Q/ZZ in the category of torsion ZZ-modules, I Q⊕ I Q/ZZ in the category ZZ-Mod, certain divisible modules over integral domains, and also cohereditary coalgebras C over a QF-ring in the category of comodules over C. Self-small tilting modules P in σ[M ] are finitely presented in σ[M ]. For M = P , they are just the ∗-modules introduced by C. Menini and A. Orsatti, and for M = R, they are the usual tilting modules considered in representation theory. Notice that our techniques and most of our results also apply to locally finitely generated Grothendieck categories.","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128373401","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 : 2019-05-16DOI: 10.1201/9780429187605-33
D. Simson
{"title":"Dualities and Pure Semisimple Rings","authors":"D. Simson","doi":"10.1201/9780429187605-33","DOIUrl":"https://doi.org/10.1201/9780429187605-33","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126887480","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 : 2019-05-16DOI: 10.1201/9780429187605-14
S. Dascalescu, C. Nastasescu, S. Raianu
{"title":"Strongly Graded Coalgebras and Crossed Coproducts","authors":"S. Dascalescu, C. Nastasescu, S. Raianu","doi":"10.1201/9780429187605-14","DOIUrl":"https://doi.org/10.1201/9780429187605-14","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124340178","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":"Adalberto Orsatti’s Contribution to Abelian Group Theory","authors":"L. Salce","doi":"10.1201/9780429187605-1","DOIUrl":"https://doi.org/10.1201/9780429187605-1","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115294932","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 : 2019-05-16DOI: 10.1201/9780429187605-30
N. Rodinò
{"title":"Cyclic Modules over End(VD ) Whose Endomorphism Ring Is an Ultrapower of D","authors":"N. Rodinò","doi":"10.1201/9780429187605-30","DOIUrl":"https://doi.org/10.1201/9780429187605-30","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131915932","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":"Idempotents of the Class Semigroup of a Prüfer Domain of Finite Character","authors":"S. Bazzoni","doi":"10.1201/9780429187605-9","DOIUrl":"https://doi.org/10.1201/9780429187605-9","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133709356","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 : 2019-05-16DOI: 10.1201/9780429187605-31
P. Ruzicka, J. Trlifaj, J. Žemlička
{"title":"Criteria of Steadiness","authors":"P. Ruzicka, J. Trlifaj, J. Žemlička","doi":"10.1201/9780429187605-31","DOIUrl":"https://doi.org/10.1201/9780429187605-31","url":null,"abstract":"","PeriodicalId":139517,"journal":{"name":"abelian groups, module theory, and topology","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134163578","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}
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