Random Motion on Finite Rings, I: Commutative Rings
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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
Universal Equivalence of Linear Groups Over Local Commutative Rings with 1/2
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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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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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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
A characterization of commutative rings whose maximal ideal spectrum is Noetherian
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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
Cayley sum graph of ideals of commutative rings
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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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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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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
Commutative L*-rings II
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DOI: 10.2989/16073606.2017.1398195
Abstract: Abstract It is shown that for several important classes of commutative rings, L∗ and O∗ are equivalent. In particular, a commutative artinian ring is L∗ if and only if it is O∗. More examples of… read more here.
Keywords: commutative rings;