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Expanding phenomena over higher dimensional matrix rings

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0 Published in 2020 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2020.02.011

Abstract: Abstract In this paper, we study the expanding phenomena in the setting of higher dimensional matrix rings. More precisely, we obtain a sum-product estimate for large subsets and show that x ( y + z… read more here.

Keywords: expanding phenomena; dimensional matrix; phenomena higher; higher dimensional ... See more keywords

Universal localization of certain matrix rings

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0 Published in 2020 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2020.106633

Abstract: Abstract The Cohn localization is a process of adjoining universal inverse morphisms to the category of R-modules over a noncommutative ring R. Finding specific models for universal localizations is, in general, difficult. For certain classes… read more here.

Keywords: triangular matrix; matrix ring; universal localization; localization ... See more keywords

Radicals of matrix rings generated by a companion matrix

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1 Published in 2017 at "Communications in Algebra"

DOI: 10.1080/00927872.2016.1233214

Abstract: ABSTRACT The radicals of full matrix rings as well as structural matrix rings have been studied extensively and there is a well-developed theory for both. Here we initiate the radical theory for another class of… read more here.

Keywords: companion matrix; radicals matrix; matrix; generated companion ... See more keywords

Associated primes and primary right ideals of generalized triangular matrix rings

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1 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1508579

Abstract: Abstract Let be an (S, R)-bimodule of the rings R and S. We determine the associated primes of a formal triangular matrix ring Indeed, we show that We then obtain necessary and sufficient conditions for… read more here.

Keywords: triangular matrix; matrix; right ideals; associated primes ... See more keywords

Gorenstein projective modules and recollements over triangular matrix rings

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0 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1775240

Abstract: Abstract Let be a triangular matrix ring with R and S rings and an R–S-bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions… read more here.

Keywords: triangular matrix; recollements triangular; projective modules; gorenstein projective ... See more keywords

Jordan Derivations of Special Subrings of Matrix Rings

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1 Published in 2019 at "Algebra Colloquium"

DOI: 10.1142/s1005386719000087

Abstract: Let K be a 2-torsion free ring with identity and Rn(K, J) be the ring of all n × n matrices over K such that the entries on and above the main diagonal are elements… read more here.

Keywords: jordan derivations; special subrings; derivations special; jordan ... See more keywords

Expanding phenomena over matrix rings

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0 Published in 2018 at "Forum Mathematicum"

DOI: 10.1515/forum-2019-0032

Abstract: Abstract In this paper, we study expanding phenomena in the setting of matrix rings. More precisely, we will prove that • if A is a set of M 2 ⁢ ( ???? q ) {M_{2}(\mathbb{F}_{q})}… read more here.

Keywords: expanding phenomena; rvert lvert; lvert rvert; rvert ... See more keywords

Functional identities on upper triangular matrix rings

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0 Published in 2020 at "Open Mathematics"

DOI: 10.1515/math-2020-0018

Abstract: Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R)… read more here.

Keywords: triangular matrix; functional identities; identities upper; upper triangular ... See more keywords

Formal Matrix Rings: Isomorphism Problem

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1 Published in 2023 at "Mathematics"

DOI: 10.3390/math11071720

Abstract: We consider the isomorphism problem for formal matrix rings over a given ring. Principal factor matrices of such rings play an important role in this case. read more here.

Keywords: isomorphism problem; matrix rings; formal matrix;

On Characterization of Tripotent Matrices in Triangular Matrix Rings

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0 Published in 2021 at "TURKISH JOURNAL OF MATHEMATICS"

DOI: 10.3906/mat-2103-109

Abstract: Let R be a ring with identity 1 whose tripotents are only −1 , 0 , and 1 . It is characterized the structure of tripotents in T (R) which is the ring of triangular… read more here.

Keywords: triangular matrix; tripotent matrices; characterization tripotent; matrices triangular ... See more keywords