Growth, relations and prime spectrum of monomial algebras

2020 ◽  
Vol 4 (1) ◽  
pp. 61-71
Author(s):  
Be'eri Greenfeld
Keyword(s):  
Prime Spectrum ◽  
Monomial Algebras

scholarly journals Decomposition of monomial algebras: Applications and algorithms

2013 ◽  
Vol 5 (1) ◽  
pp. 8-14
Author(s):  
Janko Böhm ◽  
David Eisenbud ◽  
Max Nitsche
Keyword(s):  
Monomial Algebras

Monomial Algebras

2020 ◽  
pp. 293-312
Author(s):  
Jan Okniński
Keyword(s):  
Monomial Algebras

scholarly journals ON THE CLASSICAL PRIME SPECTRUM OF LATTICE MODULES

2019 ◽  
pp. 186-198 ◽  
Author(s):  
Pradip Girase ◽  
Vandeo Borkar ◽  
Narayan Phadatare
Keyword(s):  
Prime Spectrum

Zariski Topologies on Graded Ideals

2021 ◽  
Vol 78 (1) ◽  
pp. 215-224
Author(s):  
Malik Bataineh ◽  
Azzh Saad Alshehry ◽  
Rashid Abu-Dawwas
Keyword(s):  
Commutative Ring ◽  
Zariski Topology ◽  
Topological Properties ◽  
Prime Spectrum ◽  
Algebraic Properties

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.

L-algebras and topology

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.

scholarly journals Centralizer near-rings that are rings

1995 ◽  
Vol 59 (2) ◽  
pp. 173-183 ◽  
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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