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Maximal non-pseudovaluation subrings of an integral domain
The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let R ⊂ S be an extension of domains. Then R is...
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Erratum to (δ, 2)-Primary Ideals of a Commutative Ring
In Theorem 6 of [1], if R is a von Neumann regular ring, then every 2-prime ideal of R is a prime ideal. But the converse of this implication does...
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Equations for the set of overrings of normal rings and related ring extensions
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial...
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Minimal reductions and core of ideals in pullbacks
This paper deals with minimal reductions and core of ideals in various settings of pullback constructions with the aim of building original...
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(δ, 2)-Primary Ideals of a Commutative Ring
Let R be a commutative ring with nonzero identity, let I ( R ) be the set of all ideals of R and δ : I ( R ) → I ( R ) an expansion of ideals of R defined by I ...
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Maximal non Valuation Domains in an Integral Domain
Let R be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper...
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Clean-like properties in pullbacks and amalgamation rings
We study the transfer of the notions of clean rings, weakly clean rings, almost clean rings and unit regular rings to various context of pullbacks...
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Integral domains with finitely many spectral semistar operations
Let D be a finite-dimensional integral domain, Spec( D ) be the set of prime ideals of D , and SpSS( D ) be the set of spectral semistar operations on D ....
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Valuation ideals and primary w-ideals
Let D be an integral domain, V ( D ) (resp., t-V ( D )) be the set of all valuation (resp., t -valuation) ideals of D , and w - P ( D ) be the set of primary w -i...
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Studying monoids is not enough to study multiplicative properties of rings: an elementary approach
The aim of these notes is to indicate, using very simple examples, that not all results in ring theory can be derived from monoids and that there are...
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On the Strong (A)-Rings of Mahdou and Hassani
A (commutative unital) ring R with only finitely many minimal prime ideals (for instance, a Noetherian ring) is reduced and a strong ( A )-ring if and...
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The set of prime divisors of generalized denominator ideals
Let R be a Noetherian domain with quotient field K . Let A be an integral domain which contains R and whose elements are algebraic over K . We define
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Nagata-like theorems for almost Prüfer v-multiplication domains
Let D be an integral domain and X an indeterminate over D . We show that if S is an almost splitting set of an integral domain D , then D is an APVMD...
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Graph theoretic characterizations of maximal non-valuation subrings of a field
We establish several new characterizations of maximal non-valuation subrings of a field involving several concepts of commutative algebra related to...
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Neat submodules over integral domains
Neat subgroups of abelian groups have been generalized to modules in essentially two different ways (corresponding to (a) and (b) in the...
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On bowtie rings, universal survival rings and universal lying-over rings
If ( R , M ) is a quasilocal integral domain of Krull dimension n , 1< n ≤∞, and E is the direct sum of denumerably many copies of R / M , then T := R ⋈ E is a...
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Ascending the divided and going-down properties by absolute flatness
This paper aims to show that the “going-down ring” and the “divided ring” properties ascend along flat morphisms whose co-diagonal morphisms are...
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