Results 11 to 20 of about 23,078 (295)
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Miskolc Mathematical NotesThe paper aims to present a new primary ideal in a commutative ring ...
Gulsen Ulucak +2 more
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Journal of Pure and Applied Algebra, 2008 Let \(R\) be a commutative ring with identity. This paper introduces the notion of a uniformly primary ideal. A proper ideal \(Q\) of \(R\) is uniformly primary if there exists a positive integer \(n\) such that whenever \(r,s\in R\) satisfy \(rs\in Q\), then \(s^{n}\in Q\). The smallest such \(n\) is denoted by \(\text{ord}(Q)\).
Cox, Jonathan A., Hetzel, Andrew J.
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Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings
MathematicsIn this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous
Azzh Saad Alshehry +2 more
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Cellular Binomial Ideals. Primary Decomposition of Binomial Ideals
Journal of Symbolic Computation, 2000 In addition to the work of \textit{D. Eisenbud} and \textit{B. Sturmfels} [Duke Math. J. 84, 1-45 (1996; Zbl 0873.13021)], the authors present more detailed algorithms for the binomial primary decomposition of a binomial ideal in the ring of polynomials \(K[x_1,x_2, \dots,x_n]\) over an algebraically closed field \(K\). In so doing, decompositions into
Ignacio Ojeda Martínez de Castilla +1 more
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On Primary Ideals. Part I [PDF]
Formalized Mathematics, 2021 Summary . We formalize in the Mizar System [3], [4], definitions and basic propositions about primary ideals of a commutative ring along with Chapter 4 of [1] and Chapter III of [8]. Additionally other necessary basic ideal operations such as compatibilities taking radical and intersection of finite number of ...
Watase, Yasushige
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Quasi-primary ideals in commutative semirings
Discussiones Mathematicae - General Algebra and Applications, 2023 In this paper, we define quasi-primary ideals in commutative semirings $S$ with $1\ne 0$ which is a generalization of primary ideals. A proper ideal $I$ of a semiring $S$ is said to be a quasi-primary ideal of $S$ if $ab\in \sqrt I$ implies $a\in \sqrt ...
Poonam Sarohe, Pratibha Kumar
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$(\delta, 2)$-primary ideals of a commutative ring [PDF]
, 2020 summary:Let $R$ be a commutative ring with nonzero identity, let $\mathcal {I(R)}$ be the set of all ideals of $R$ and $\delta \colon \mathcal {I(R)}\rightarrow \mathcal {I(R)}$ an expansion of ideals of $R$ defined by $I\mapsto \delta (I)$. We introduce
Çelikel, Ece Yetkin +2 more
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-primary ideals of commutative rings [PDF]
, 2023 Let R be a commutative ring with 1 not equal 0 and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasi-S-primary if there exists an s is an element of S such that whenever a, b is an element of R and ab is an element
Hamed, Ahmed +3 more
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On certain generalized prime ideals in boolean like semiring of fractions [PDF]
Journal of Hyperstructures, 2014 In this paper, we introduce the notions of semiprime ideals, 2-potent prime ideals, weakly prime ideals and weakly primary ideals in a Boolean like semiring of fractions. Further, we obtain various results concerning the notions.
K. H. Demissie +2 more
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On Weakly 1-Absorbing Primary Ideals of Commutative Semirings
Communications in Advanced Mathematical Sciences, 2022 Let $R$ be a commutative semiring with $ 1 \neq0$. In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal over commutative semirings . A proper ideal $I$ of a semiring $R$ is called a weakly
Ibaa Muraa, Mohammad Saleh
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