scholarly journals Sub-prime radical classes determined by zerorings

1975 ◽  
Vol 12 (1) ◽  
pp. 95-97 ◽  
Author(s):  
B.J. Gardner
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Prime Radical ◽  
Radical Class

It is shown that the correspondence which associates with each radical class τ of abelian groups the (radical) class of prime radical rings with additive groups in τ gives a complete classification of those radical classes of rings which are determined (as lower radicals) by zerorings.

Groups Admitting only Finitely Many Nilpotent Ring Structures

1986 ◽  
Vol 29 (2) ◽  
pp. 197-203
Author(s):  
Shalom Feigelstock
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Actual Number ◽  
Nilpotent Ring ◽  
Ring Structures ◽  
Free Case ◽  
Torsion Free

AbstractThe abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.

scholarly journals CONVEXLY ORDERABLE GROUPS AND VALUED FIELDS

2014 ◽  
Vol 79 (01) ◽  
pp. 154-170
Author(s):  
JOSEPH FLENNER ◽  
VINCENT GUINGONA
Keyword(s):  
Abelian Groups ◽  
Complete Classification ◽  
Necessary Condition ◽  
Valued Fields ◽  
Ordered Groups ◽  
Algebraic Theories ◽  
Convexly Orderable

Abstract We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also considered, including a necessary condition for a theory of valued fields to be quasi-VC-minimal. For example, the p-adics are not quasi-VC-minimal.

Orderings in locally compact Abelian groups and the theorem of F. and M. Riesz

1983 ◽  
Vol 93 (3) ◽  
pp. 441-457 ◽  
Author(s):  
Edwin Hewitt ◽  
Shozo Koshi
Keyword(s):  
Harmonic Analysis ◽  
Abelian Groups ◽  
Complete Classification ◽  
Locally Compact ◽  
Locally Compact Abelian Groups ◽  
Compact Abelian Groups

Background (1·1). Ordered Abelian groups have been studied for nearly a century. Since the early 1950's, it has been recognized that orderings in locally compact Abelian groups can play an important rôle in harmonic analysis on such groups. In this paper we study orderings, especially in topological Abelian groups with either topological or measure-theoretic properties, obtaining nearly a complete classification of such orderings. We then apply these results to determine the limitations of the celebrated theorem of F. and M. Riesz on such groups.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

scholarly journals ABELIAN GROUPS WITH A p2-BOUNDED SUBGROUP, REVISITED

2011 ◽  
Vol 10 (03) ◽  
pp. 377-389
Author(s):  
CARLA PETRORO ◽  
MARKUS SCHMIDMEIER
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Maximal Ideal ◽  
Abelian Groups ◽  
Finitely Generated ◽  
Uniserial Ring

Let Λ be a commutative local uniserial ring of length n, p be a generator of the maximal ideal, and k be the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆B a submodule of B such that pmA = 0 form the objects in the category [Formula: see text]. We show that in case m = 2 the categories [Formula: see text] are in fact quite similar to each other: If also Δ is a commutative local uniserial ring of length n and with radical factor field k, then the categories [Formula: see text] and [Formula: see text] are equivalent for certain nilpotent categorical ideals [Formula: see text] and [Formula: see text]. As an application, we recover the known classification of all pairs (B, A) where B is a finitely generated abelian group and A ⊆ B a subgroup of B which is p2-bounded for a given prime number p.

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

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