Results 11 to 20 of about 137 (99)
, 2000 We explore new closure operations on sets of ideals in a commutative Noetherian ring of characteristic p, related to tight and integral closure. We develop the theories of multiple closure and blowup closure of a set of ideals.
Faridi, Sara
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, 2002 Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and ...
Vasantha, Kandasamy
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, 2023 summary:Let $D$ be an integral domain with the quotient field $K$, $X$ an indeterminate over $K$ and $x$ an element of $D$. The Bhargava ring over $D$ at $x$ is defined to be $\mathbb {B}_x(D):=\{f\in \nobreak K[X]\colon \text {for all}\ a\in D,\ f(xX+a)
Ouzzaouit, Omar +2 more
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Commutative rings with finitely generated monoids of fractional ideals [PDF]
, 2008 Let R be a commutative ring with identity and let P(R) be the monoid of principal fractional ideals of R. We show that P(R) is finitely generated if and only if P(R¯) (R¯ the integral closure of R) is finitely generated and R¯/[R:R¯] is finite. Moreover,
Anderson, D.D., Chun, S.
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Rings with two-generated ideals [PDF]
, 1991 A commutative ring R is said to have the two-generator property if each ideal of R can be generated by two elements, and is said to be stable if each regular ideal of R is projective over its endomorphism ring.
Rush, David E., David E. Rush
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Closure Operations on Ideals in Commutative Rings [PDF]
, 2009 A closure operation is an idempotent endomorphism on the set of ideals of a given [commutative Noetherian] ring, which produces an ideal that contains the given ideal, and preserves containment of ideals.
Epstein, Neil
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Smarandache semirings, semifields, and semivector spaces [PDF]
, 2002 Smarandache notions, which can be undoubtedly characterized as interesting mathematics, has the capacity of being utilized to analyse, study and introduce, naturally, the concepts of several structures by means of extension or identification as a ...
Vasantha, Kandasamy
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Proper spaces are spectral [PDF]
, 2023 [EN] Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower ...
Goswami, Amartya
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Blow-up algebras in Algebra, Geometry and Combinatorics [PDF]
, 2019 [eng] The primary topic of this thesis lies at the crossroads of Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. It is mainly focused around the following themes: I Defining equations of blow-up algebras.
Cid Ruiz, Yairon
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Equations for the set of overrings of normal rings and related ring extensions
, 2023 summary:We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions.
Jaballah, Ali, Ben Nasr, Mabrouk
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