On the finite prime spectrum minimal groups

2016 ◽  
Vol 295 (S1) ◽  
pp. 109-119
Author(s):  
N. V. Maslova
Keyword(s):  
Prime Spectrum ◽  
Minimal Groups

scholarly journals ON THE STRUCTURE OF GROUPS ENDOWED WITH A COMPATIBLE C-RELATION

2018 ◽  
Vol 83 (3) ◽  
pp. 939-966
Author(s):  
GABRIEL LEHÉRICY
Keyword(s):  
Ordered Groups ◽  
Quasi Order ◽  
Minimal Groups

AbstractWe use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of quasi-orders some results concerning C-minimal groups given in [5].

scholarly journals ON REGULAR GROUPS AND FIELDS

2014 ◽  
Vol 79 (3) ◽  
pp. 826-844 ◽  
Author(s):  
TOMASZ GOGACZ ◽  
KRZYSZTOF KRUPIŃSKI
Keyword(s):  
Conjugacy Class ◽  
Classical Group ◽  
Multiplicative Group ◽  
Finite Extension ◽  
Generic Type ◽  
Common Generalization ◽  
Counter Example ◽  
Minimal Groups ◽  
Unbounded Orbit

AbstractRegular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenP(n)has unbounded orbit under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable.

Emotions of my kin: disambiguating expressive body movement in minimal groups

2016 ◽  
Vol 4 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Gary Bente ◽  
Daniel Roth ◽  
Thomas Dratsch ◽  
Kai Kaspar
Keyword(s):  
Body Movement ◽  
Minimal Groups ◽  
Expressive Body Movement

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

scholarly journals On non-abelian C-minimal groups

2003 ◽  
Vol 122 (1-3) ◽  
pp. 263-287 ◽  
Author(s):  
Patrick Simonetta
Keyword(s):  
Minimal Groups

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.

scholarly journals On the importance of being primitive

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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