{"title":"Tschirnhaus transformation and a new approach to solve the 4th degree algebraic equation","authors":"E. Salinas-Hernández, G. Ares de Parga","doi":"10.12988/ija.2021.91577","DOIUrl":"https://doi.org/10.12988/ija.2021.91577","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74569474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present the concept of Brauer morphism in the quandle G-algebra setting together with an illustration example of this construction. We study the relationship between the relative trace map and the Brauer morphism. We introduce the concept of the defect group of a primitive idempotent by using the relative trace map and the Brauer morphism. The object of an interior quandle G-algebra is studied, as well as, we define the homomorphism of interior quandle G-algebras. Mathematics Subject Classification: Primary 20N02, Secondary 20B25
{"title":"Brauer quotient of interior quandle G-algebra","authors":"Amani M. Alfadhli, A. Alghamdi","doi":"10.12988/IJA.2021.91277","DOIUrl":"https://doi.org/10.12988/IJA.2021.91277","url":null,"abstract":"In this paper, we present the concept of Brauer morphism in the quandle G-algebra setting together with an illustration example of this construction. We study the relationship between the relative trace map and the Brauer morphism. We introduce the concept of the defect group of a primitive idempotent by using the relative trace map and the Brauer morphism. The object of an interior quandle G-algebra is studied, as well as, we define the homomorphism of interior quandle G-algebras. Mathematics Subject Classification: Primary 20N02, Secondary 20B25","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79448139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is well known that tilting modules of projective dimension not more than 1 coincide with ∗-modules generating all injective modules. Later, Wei et al. introduced the notion of ∗n-modules as the generalizations of ∗-modules. Yao and Chen introduced the dual situation of ∗n-modules which are called co-∗n-modules. In this paper, we present some properties of co-∗n-modules. Mathematics Subject Classification: Primary 16D90 Secondary 16E05 16E10
{"title":"A note on co-*n-modules","authors":"Yu‐Qin Mei, Jiaqun Wei","doi":"10.12988/ija.2021.91571","DOIUrl":"https://doi.org/10.12988/ija.2021.91571","url":null,"abstract":"It is well known that tilting modules of projective dimension not more than 1 coincide with ∗-modules generating all injective modules. Later, Wei et al. introduced the notion of ∗n-modules as the generalizations of ∗-modules. Yao and Chen introduced the dual situation of ∗n-modules which are called co-∗n-modules. In this paper, we present some properties of co-∗n-modules. Mathematics Subject Classification: Primary 16D90 Secondary 16E05 16E10","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79255280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study some results on the ideal theory of commutative Γ− semirings analogues to commutative semirings . In particular, Q-ideals , maximal ideals, primary ideals and radical ideals of commutative Γ− semiring are investigated . Furthermore we make an intensive examination of the notions of maximal ideal and local Γ− semirings. It is shown that the notion of primary ideals in Γ− semirings inherits most of essential properties of primary ideals of commutative semirings. Mathematics Subject Classification: 16Y60, 16Y99
{"title":"Ideal theory in commutative Γ - semirings","authors":"W. Fakieh, Fatimah A. Alhawiti","doi":"10.12988/IJA.2021.91527","DOIUrl":"https://doi.org/10.12988/IJA.2021.91527","url":null,"abstract":"In this paper, we study some results on the ideal theory of commutative Γ− semirings analogues to commutative semirings . In particular, Q-ideals , maximal ideals, primary ideals and radical ideals of commutative Γ− semiring are investigated . Furthermore we make an intensive examination of the notions of maximal ideal and local Γ− semirings. It is shown that the notion of primary ideals in Γ− semirings inherits most of essential properties of primary ideals of commutative semirings. Mathematics Subject Classification: 16Y60, 16Y99","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82837920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let K be a field of characteristics p > 2. Giambruno and Koshlukov have proved [2] that Grassmann Algebra E satisfies the standard identity of degree m if, and only if, m ≥ p + 1. The object of this paper is to extend such result to E ⊗ E, more precisely proving that E ⊗ E satisfies the standard identity of degree m if, and only if, m ≥ 2p. Mathematics Subject Classification: 15A75, 16R20
{"title":"The minimal degree standard identity on E ⊗ E","authors":"Geraldo de Assis Junior, Sergio Mota Alves","doi":"10.12988/ija.2021.91572","DOIUrl":"https://doi.org/10.12988/ija.2021.91572","url":null,"abstract":"Let K be a field of characteristics p > 2. Giambruno and Koshlukov have proved [2] that Grassmann Algebra E satisfies the standard identity of degree m if, and only if, m ≥ p + 1. The object of this paper is to extend such result to E ⊗ E, more precisely proving that E ⊗ E satisfies the standard identity of degree m if, and only if, m ≥ 2p. Mathematics Subject Classification: 15A75, 16R20","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88880530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Diaz-Vargas, Carlos Jacob Rubio-Barrios, H. Tapia-Recillas, Juan Armando Velazco-Velazco
{"title":"Linear codes over the ring Rm = Z2m + uZ2m","authors":"J. Diaz-Vargas, Carlos Jacob Rubio-Barrios, H. Tapia-Recillas, Juan Armando Velazco-Velazco","doi":"10.12988/ija.2021.91568","DOIUrl":"https://doi.org/10.12988/ija.2021.91568","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86860708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.35940/IJAC.B2007.101221
G. Badilla, J. T. Gaynor
{"title":"The Electronics Industry and Their Chemical Effects in the Environment of Arid Regions ofNorthwest of Mexico","authors":"G. Badilla, J. T. Gaynor","doi":"10.35940/IJAC.B2007.101221","DOIUrl":"https://doi.org/10.35940/IJAC.B2007.101221","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70082793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We determine all primitive simple permutation groups with suborbit length 5 which have a faithful subconstituent of A5. Mathematics Subject Classification: 05C25, 20B25
{"title":"Primitive simple permutation group with A5 as a faithful subconstituent","authors":"Zhengfei Wu, Shangjin Xu","doi":"10.12988/IJA.2021.91546","DOIUrl":"https://doi.org/10.12988/IJA.2021.91546","url":null,"abstract":"We determine all primitive simple permutation groups with suborbit length 5 which have a faithful subconstituent of A5. Mathematics Subject Classification: 05C25, 20B25","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72665980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ousmane Djiby Diallo, Mohamed Ben Faraj Ben Maaouia, M. Sanghare
The main results we show in this paper are: • if A is a ring, S a saturated multiplicative set of A which satisfies the left Ore conditions then the category S−1A−Mod of the left S−1A-modules is equivalent to the category of left A-modules S-divisible and S-torsion free (denoted by STDA−Mod). • If A and B are Morita equivalent rings (denoted A ≈ B) and if S is a central saturated multiplicative set of A then the rings S−1A and S−1B are Morita equivalent and for any (two-sided) ideal I of A, if J is the ideal of B corresponding to I, then S−1I is an ideal of S−1A corresponding to the ideal S−1J of S−1B. • IfA ≈ B then the categories of complexes Comp(A−Mod) and Comp(B −Mod) are equivalent ( Comp(A−Mod) ≈ Comp(B −Mod) for short) and for all central multiplicative set S of A, 138 O. D. Diallo, M. B. Maaouia and M. Sanghare Comp ( S−1A−Mod ) ≈ Comp ( S−1B −Mod )
本文得到的主要结果是:•如果A是环，S是满足左Ore条件的A的饱和乘集，则左S- 1A-模的范畴S−1A−Mod等价于左A模的范畴S-可分且S-无扭(用STDA−Mod表示)。•如果A和B是森田等价环(记为A≈B)，如果S是A的中心饱和乘法集，则环S−1A和S−1B是森田等价环，对于A的任何(双面)理想I，如果J是B的理想对应于I，则S−1I是S−1A的理想对应于S−1B的理想S−1J。•IfA≈B，则配合物Comp(A−Mod)和Comp(B−Mod)的范畴是等价的(简称Comp(A−Mod)≈Comp(B−Mod))，并且对于A的所有中心乘法集S, 138 O. D. Diallo, M. B. Maaouia和M. Sanghare Comp(S−1A−Mod)≈Comp(S−1B−Mod)
{"title":"Functor localization S-1() and Morita theory of category equivalences","authors":"Ousmane Djiby Diallo, Mohamed Ben Faraj Ben Maaouia, M. Sanghare","doi":"10.12988/IJA.2021.91531","DOIUrl":"https://doi.org/10.12988/IJA.2021.91531","url":null,"abstract":"The main results we show in this paper are: • if A is a ring, S a saturated multiplicative set of A which satisfies the left Ore conditions then the category S−1A−Mod of the left S−1A-modules is equivalent to the category of left A-modules S-divisible and S-torsion free (denoted by STDA−Mod). • If A and B are Morita equivalent rings (denoted A ≈ B) and if S is a central saturated multiplicative set of A then the rings S−1A and S−1B are Morita equivalent and for any (two-sided) ideal I of A, if J is the ideal of B corresponding to I, then S−1I is an ideal of S−1A corresponding to the ideal S−1J of S−1B. • IfA ≈ B then the categories of complexes Comp(A−Mod) and Comp(B −Mod) are equivalent ( Comp(A−Mod) ≈ Comp(B −Mod) for short) and for all central multiplicative set S of A, 138 O. D. Diallo, M. B. Maaouia and M. Sanghare Comp ( S−1A−Mod ) ≈ Comp ( S−1B −Mod )","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83510199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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