On the lattice of z-ideals of a commutative ring
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DOI: 10.1016/j.topol.2019.106969
Abstract: Abstract We prove that the lattice of z-ideals of a commutative ring with identity is a coherent frame. We characterize when it is a Yosida frame, and when it satisfies some projectability properties. We also… read more here.
Keywords: lattice ideals; ideals commutative; frame; commutative ring ... See more keywords
Naive-commutative ring structure on rational equivariant K-theory for abelian groups
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DOI: 10.1016/j.topol.2022.108100
Abstract: In this paper, we calculate the image of the connective and periodic rational equivariant complex $K$-theory spectrum in the algebraic model for naive-commutative ring $G$-spectra given by Barnes, Greenlees and K\k{e}dziorek for finite abelian $G$.… read more here.
Keywords: naive commutative; rational equivariant; theory; structure ... See more keywords
A new semistar operation on a commutative ring and its applications
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DOI: 10.1080/00927872.2020.1753060
Abstract: Abstract In this article, a new semistar operation, called the q-operation, on a commutative ring R is introduced in terms of the ring of finite fractions. It is defined as the map by there exists… read more here.
Keywords: new semistar; semistar operation; operation commutative; operation ... See more keywords
The dimension graph of a commutative ring
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DOI: 10.1080/00927872.2024.2362931
Abstract: Abstract This paper introduces a simple graph associated to a commutative ring. Nonzero ideals I and J of a commutative ring R are called Krull dimension-dependent whenever dimR/(I+J)=min{dimR/I,dimR/J} . Based on this, we introduce the… read more here.
Keywords: dimension graph; commutative ring; dimension; graph commutative ... See more keywords
On double chains and inverse double chains of modules over a commutative ring
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DOI: 10.1080/00927872.2025.2461273
Abstract: Abstract We consider infinite double chains ⋯N−1⊂N0⊂N1⊂⋯ and infinite inverse double chains N0⊂N1⊂N2⊂⋯⋯⊂M2⊂M1⊂M0 of submodules of a module M over a commutative ring R. We shall give conditions under which such chains exist. Examples show… read more here.
Keywords: commutative ring; chains inverse; double chains; inverse double ... See more keywords
Brauer groups and Galois cohomology of commutative ring spectra
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DOI: 10.1112/s0010437x21007065
Abstract: In this paper we develop methods for classifying Baker, Richter, and Szymik's Azumaya algebras over a commutative ring spectrum, especially in the largely inaccessible case where the ring is nonconnective. We give obstruction-theoretic tools, constructing… read more here.
Keywords: algebraic azumaya; equivalence; azumaya algebras; ring spectra ... See more keywords
Associate class graph of zero-divisors of a commutative ring
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DOI: 10.1142/s0219498820501558
Abstract: In this paper, we introduce the concept of the associate class graph of zero-divisors of a commutative ring [Formula: see text], denoted by [Formula: see text]. Some properties of [Formula: see text], including the diameter,… read more here.
Keywords: class graph; associate class; graph zero; graph ... See more keywords
Square-Difference Factor Absorbing Ideals of a Commutative Ring
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DOI: 10.1142/s0219498826501987
Abstract: Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if whenever $a^2 - b^2 \in I$ for… read more here.
Keywords: commutative ring; absorbing ideals; factor absorbing; square difference ... See more keywords
The essential ideal graph of a commutative ring
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DOI: 10.1142/s1793557118500584
Abstract: Let R be a commutative ring with identity. The essential ideal graph of R, denoted by ℰR, is a graph whose vertex set is the set of all nonzero proper ideals of R and two… read more here.
Keywords: graph commutative; essential ideal; graph; ideal graph ... See more keywords
Ideal‐Based Quasi Cozero Divisor Graph of a Commutative Ring
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DOI: 10.1155/jom/4415087
Abstract: Let R be a commutative ring with identity and I be an ideal of R . The zero‐divisor graph of R with respect to I , denoted by Γ I ( R ), is the… read more here.
Keywords: italic jats; commutative ring; jats italic; divisor graph ... See more keywords
Some properties of the total graph and regular graph of a commutative ring
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DOI: 10.15672/hjms.2017.490
Abstract: Let $R$ be a commutative ring with unity. The total graph of $R$, $T(\Gamma(R))$, is the simple graph with vertex set $R$ and two distinct vertices are adjacent if their sum is a zero-divisor in… read more here.
Keywords: reg gamma; graph; gamma gamma; gamma ... See more keywords