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   Articles with "commutative rings" as a keyword



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Random Motion on Finite Rings, I: Commutative Rings

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recommendations! Published in 2019 at "Algebras and Representation Theory"

DOI: 10.1007/s10468-019-09864-w

Abstract: We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first prove… read more here.

Keywords: commutative rings; random motion; multiplication; rings commutative ... See more keywords
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Universal Equivalence of Linear Groups Over Local Commutative Rings with 1/2

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recommendations! Published in 2019 at "Algebra and Logic"

DOI: 10.1007/s10469-019-09552-0

Abstract: It is proved that the universal equivalence of general or special linear groups of orders greater than 2 over local commutative rings with 1/2 is equivalent to the coincidence of orders of groups and universal… read more here.

Keywords: commutative rings; linear groups; universal equivalence; equivalence linear ... See more keywords

Schur–Weyl duality over commutative rings

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recommendations! Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1513010

Abstract: Abstract The classical case of Schur–Weyl duality states that the actions of the group algebras of GLn and Sd on the dth-tensor power of a free module of finite rank centralize each other. We show… read more here.

Keywords: weyl duality; commutative rings; duality commutative; schur weyl ... See more keywords

Structure of virtually semisimple modules over commutative rings

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recommendations! Published in 2020 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1723611

Abstract: Abstract Modules in which every submodule is isomorphic to a direct summand is called virtually semisimple. In this article, we carry out a study of virtually semisimple modules over a commutative ring R. A structure… read more here.

Keywords: commutative rings; structure virtually; semisimple modules; virtually semisimple ... See more keywords

When every S-flat module is (flat) projective

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recommendations! Published in 2024 at "Communications in Algebra"

DOI: 10.1080/00927872.2024.2348126

Abstract: Abstract Let R be a commutative ring with identity and S a multiplicative subset of R. The aim of this paper is to study the class of commutative rings in which every S-flat module is… read more here.

Keywords: every flat; module; flat module; flat projective ... See more keywords

Commutative rings in which every S-finite ideal is projective

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recommendations! Published in 2024 at "Communications in Algebra"

DOI: 10.1080/00927872.2024.2398623

Abstract: Abstract In this paper, we introduce and explore a category of rings termed SFP-rings, defined by the property that each S-finite ideal of them is projective. We demonstrate that all hereditary rings inherently qualify as… read more here.

Keywords: rings every; sfp rings; every finite; ideal projective ... See more keywords
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A characterization of commutative rings whose maximal ideal spectrum is Noetherian

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recommendations! Published in 2018 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498818500032

Abstract: An ideal I of a ring R is called pseudo-irreducible if I cannot be written as an intersection of two comaximal proper ideals of R. In this paper, it is shown that the maximal spectrum… read more here.

Keywords: commutative rings; ideal; spectrum noetherian; rings whose ... See more keywords
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Cayley sum graph of ideals of commutative rings

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recommendations! Published in 2017 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498818501256

Abstract: Let R be a commutative ring, ℐ(R) the set of all ideals of R and S, a subset of ℐ∗(R) = ℐ(R)∖{0}. The Cayley sum graph of ideals of R, denoted by Cay(ℐ(R),S), is a… read more here.

Keywords: commutative rings; cayley sum; ideals commutative; graph ... See more keywords

Commutative rings whose ideal lattices are complemented

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recommendations! Published in 2019 at "Asian-European Journal of Mathematics"

DOI: 10.1142/s1793557119500396

Abstract: We characterize those commutative rings [Formula: see text] whose ideal lattice [Formula: see text] endowed with the annihilation operation is an ortholattice. Moreover, we provide an analogous characterization for the annihilator lattice [Formula: see text]… read more here.

Keywords: whose ideal; commutative rings; rings whose; formula see ... See more keywords

On 2-Absorbing Primary Fuzzy Ideals of Commutative Rings

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recommendations! Published in 2017 at "Mathematical Problems in Engineering"

DOI: 10.1155/2017/5485839

Abstract: In this work, we give a characterization of generalizations of prime and primary fuzzy ideals by introducing 2-absorbing fuzzy ideals and 2-absorbing primary fuzzy ideals and establish relations between 2-absorbing (primary) fuzzy ideals and 2-absorbing… read more here.

Keywords: absorbing primary; fuzzy ideals; commutative rings; ideals commutative ... See more keywords

More on the weakly 2-prime ideals of commutative rings

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recommendations! Published in 2024 at "Filomat"

DOI: 10.2298/fil2417099i

Abstract: Let R be a commutative ring with a nonzero identity. In this paper, we introduce the concept of weakly 2-prime ideal which is a generalization of 2-prime ideal and both are generalizations of prime ideals.… read more here.

Keywords: prime ideals; prime ideal; commutative rings; ideals commutative ... See more keywords