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
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
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
Some properties of the total graph and regular graph of a commutative ring
Sign Up to like & getrecommendations! Published in 2017 at "Hacettepe Journal of Mathematics and Statistics"
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