Pseudocomplementation and minimal prime ideals in semirings
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DOI: 10.1007/s00012-018-0496-x
Abstract: In Section 2 of the present paper, we introduce the concept of pseudocomplementation for semirings and show the semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove… read more here.
Keywords: ideals semirings; theory; pseudocomplementation minimal; prime ideals ... See more keywords
Regularity of prime ideals
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DOI: 10.1007/s00209-018-2089-y
Abstract: We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud–Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not… read more here.
Keywords: prime ideals; regularity prime; regularity;
The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series
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DOI: 10.1007/s11139-021-00404-z
Abstract: We prove that for a graded algebra $$\mathcal {A}$$ with a derivation $$D_{\mathcal {A}}$$ satisfying certain conditions, and a bi-graded algebra $$\mathcal {A}[q]$$ with an extended derivation D of $$D_{\mathcal {A}}$$ , there are only… read more here.
Keywords: algebraic independence; derivation; eisenstein series; prime ideals ... See more keywords
On almost fuzzy prime ideals and sub-modules
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DOI: 10.1007/s13370-019-00670-7
Abstract: The purpose of this paper is to present some characterizations of almost fuzzy prime ideals and sub modules; and to introduce certain innovative fuzzy prime ideals and sub modules respectively. Moreover, every fuzzy ideal in… read more here.
Keywords: fuzzy prime; ideals sub; almost fuzzy; prime ideals ... See more keywords
THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V2)
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DOI: 10.1017/s0017089519000302
Abstract: Abstract Let 𝔟 be the Borel subalgebra of the Lie algebra 𝔰𝔩2 and V2 be the simple two-dimensional 𝔰𝔩2-module. For the universal enveloping algebra $\[{\cal A}: = U(\gb \ltimes {V_2})\]$ of the semi-direct product 𝔟⋉V2… read more here.
Keywords: prime ideals; universal enveloping; simple modules; modules universal ... See more keywords
Attached prime ideals of generalized inverse polynomial modules
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DOI: 10.1142/s1793557117500231
Abstract: Let R be a ring, (S,≤) a strictly totally ordered monoid which is also artinian and ω : S →Aut(R) a monoid homomorphism. Given a right R-module M, denote by [MS,≤] [[RS,≤,ω]] the generalized inverse… read more here.
Keywords: generalized inverse; module; attached prime; inverse polynomial ... See more keywords
Characterization of prime ideals, filters in ABAs
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DOI: 10.1142/s1793557120501065
Abstract: In this paper, we discuss several properties of ideals, filters, annihilators and maximisors in a general Almost Distributive Lattices (ADLs) and in particular, Almost Boolean Algebras (ABAs). Also, we characterize extreme ideals and filters. Further,… read more here.
Keywords: ideals filters; prime ideals; characterization prime; filters abas ... See more keywords
Fuzzy Prime Ideals of ADL's
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DOI: 10.12962/j24775401.v4i2.3187
Abstract: In this paper the concept of prime L-fuzzy ideals and L-fuzzy prime ideals of an ADL A with truth values in a complete lattice L satisfying the infinite meet distributive law are introduced. All prime… read more here.
Keywords: fuzzy ideals; prime fuzzy; fuzzy prime; prime ideals ... See more keywords
WEAKLY PRIME IDEALS ISSUED FROM AMALGAMATED ALGEBRA
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DOI: 10.15672/hujms.557437
Abstract: Let $R$ be a commutative ring with identity. A proper ideal $P$ is said to be weakly prime ideal of $R$ if for every $0\neq ab\in P$ where $a,b\in R,$ implies $a\in P$ or $b\in… read more here.
Keywords: ideal; weakly prime; amalgamated algebra; issued amalgamated ... See more keywords