Prime spectrum of a tetravalent modal algebra.

Abstract In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring R and topological properties of open subsets of Zariski topology on the graded prime spectrum of R. We examine some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense, and irreducible. We also present a characterization for the radical of a graded ideal in R by using topological properties.

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L-algebras and topology

Journal of Algebra and Its Applications ◽

10.1142/s0219498823500342 ◽

2021 ◽

Author(s):

Wolfgang Rump

Keyword(s):

Mapping Class Groups ◽

Unitary Groups ◽

Mapping Class ◽

Heyting Algebras ◽

Baxter Equation ◽

Prime Spectrum ◽

Class Groups ◽

Orthomodular Lattices ◽

And Topology ◽

Torsion Free

[Formula: see text]-algebras are based on an equation which is fundamental in the construction of various torsion-free groups, including spherical Artin groups, Riesz groups, certain mapping class groups, para-unitary groups, and structure groups of set-theoretic solutions to the Yang–Baxter equation. A topological study of [Formula: see text]-algebras is initiated. A prime spectrum is associated to certain (possibly all) [Formula: see text]-algebras, including three classes of [Formula: see text]-algebras where the ideals are determined in a more explicite fashion. Known results on orthomodular lattices, Heyting algebras, or quantales are extended and revisited from an [Formula: see text]-algebraic perspective.

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Centralizer near-rings that are rings

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s144678870003857x ◽

1995 ◽

Vol 59 (2) ◽

pp. 173-183 ◽

Cited By ~ 24

Author(s):

Jutta Hausen ◽

Johnny A. Johnson

Keyword(s):

Endomorphism Ring ◽

Sufficient Conditions ◽

Dedekind Domain ◽

Prime Spectrum ◽

Dedekind Domains ◽

Composition Of Functions

AbstractGiven an R-module M, the centralizer near-ring ℳR (M) is the set of all functions f: M → M with f(xr)= f(x)r for all x ∈ M and r∈R endowed with point-wise addition and composition of functions as multiplication. In general, ℳR(M) is not a ring but is a near-ring containing the endomorphism ring ER(M) of M. Necessary and/or sufficient conditions are derived for ℳR(M) to be a ring. For the case that R is a Dedekind domain, the R-modules M are characterized for which (i) ℳR(M) is a ring; and (ii)ℳR(M) = ER(M). It is shown that over Dedekind domains with finite prime spectrum properties (i) and (ii) are equivalent.

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On the importance of being primitive

Revista Colombiana de Matemáticas ◽

10.15446/recolma.v53nsupl.84009 ◽

2019 ◽

Vol 53 (supl) ◽

pp. 87-112

Author(s):

Jason Bell

Keyword(s):

Ring Theory ◽

Prime Spectrum ◽

Primitive Ideals

We give a brief survey of primitivity in ring theory and in particular look at characterizations of primitive ideals in the prime spectrum for various classes of rings.

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