Acyclicity of Schur complexes and torsion freeness of Schur modules

2019 ◽  
Vol 535 ◽  
pp. 133-158
Author(s):  
Muberra Allahverdi ◽  
Alexandre Tchernev
Keyword(s):  
Torsion Freeness

Murley Groups and the Torsion-Freeness of Ext

2015 ◽  
Vol 43 (3) ◽  
pp. 1194-1206
Author(s):  
Ulrich Albrecht ◽  
Stefan Friedenberg
Keyword(s):  
Torsion Freeness

Superficial ideals for monomial ideals

2018 ◽  
Vol 17 (06) ◽  
pp. 1850102 ◽  
Author(s):  
Saeed Rajaee ◽  
Mehrdad Nasernejad ◽  
Ibrahim Al-Ayyoub
Keyword(s):  
Noetherian Ring ◽  
Monomial Ideals ◽  
Minimal Set ◽  
Commutative Noetherian Ring ◽  
Ideal Formula ◽  
Torsion Freeness ◽  
Positive Integers

Let [Formula: see text] and [Formula: see text] be two ideals in a commutative Noetherian ring [Formula: see text]. We say that [Formula: see text] is a superficial ideal for [Formula: see text] if the following conditions are satisfied: (i) [Formula: see text], where [Formula: see text] denotes a minimal set of generators of an ideal [Formula: see text]. (ii) [Formula: see text] for all positive integers [Formula: see text]. In this paper, by using some monomial operators, we first introduce several methods for constructing new ideals which have superficial ideals. In the sequel, we present some examples of monomial ideals which have superficial ideals. Next, we discuss on the relation between superficiality and normality. Finally, we explore the relation between normally torsion-freeness and superficiality.

scholarly journals Residually finite rationally p groups

2019 ◽  
Vol 22 (03) ◽  
pp. 1950016
Author(s):  
Thomas Koberda ◽  
Alexander I. Suciu
Keyword(s):  
Algebraic Geometry ◽  
Group Theory ◽  
Large Class ◽  
Algebraic Curves ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Residual Property ◽  
Residually Finite ◽  
Torsion Freeness ◽  
Do So

In this paper, we develop the theory of residually finite rationally [Formula: see text] (RFR[Formula: see text]) groups, where [Formula: see text] is a prime. We first prove a series of results about the structure of finitely generated RFR[Formula: see text] groups (either for a single prime [Formula: see text], or for infinitely many primes), including torsion-freeness, a Tits alternative, and a restriction on the BNS invariant. Furthermore, we show that many groups which occur naturally in group theory, algebraic geometry, and in 3-manifold topology enjoy this residual property. We then prove a combination theorem for RFR[Formula: see text] groups, which we use to study the boundary manifolds of algebraic curves [Formula: see text] and in [Formula: see text]. We show that boundary manifolds of a large class of curves in [Formula: see text] (which includes all line arrangements) have RFR[Formula: see text] fundamental groups, whereas boundary manifolds of curves in [Formula: see text] may fail to do so.

scholarly journals Resource convertibility and ordered commutative monoids

2015 ◽  
Vol 27 (6) ◽  
pp. 850-938 ◽  
Author(s):  
TOBIAS FRITZ
Keyword(s):  
Information Theory ◽  
Communication Channel ◽  
Linear Logic ◽  
Commutative Monoids ◽  
Science And Engineering ◽  
Von Neumann ◽  
Torsion Freeness ◽  
Equality Relation ◽  
Image Position ◽  
Reaction Equations

Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For example, information theory studies the conversion of a noisy communication channel instance into an exchange of information. Inspired by work in quantum information theory, we develop a general mathematical toolbox for this type of question. The convertibility of resources into other ones and the possibility of combining resources is accurately captured by the mathematics of ordered commutative monoids. As an intuitive example, we consider chemistry, where chemical reaction equations such as\mathrm{2H_2 + O_2} \lra \mathrm{2H_2O,}are concerned both with a convertibility relation ‘→’ and a combination operation ‘+.’ We study ordered commutative monoids from an algebraic and functional-analytic perspective and derive a wealth of results which should have applications to concrete resource theories, such as a formula for rates of conversion. As a running example showing that ordered commutative monoids are also of purely mathematical interest without the resource-theoretic interpretation, we exemplify our results with the ordered commutative monoid of graphs.While closely related to both Girard's linear logic and to Deutsch's constructor theory, our framework also produces results very reminiscent of the utility theorem of von Neumann and Morgenstern in decision theory and of a theorem of Lieb and Yngvason on the foundations of thermodynamics.Concerning pure algebra, our observation is that some pieces of algebra can be developed in a context in which equality is not necessarily symmetric, i.e. in which the equality relation is replaced by an ordering relation. For example, notions like cancellativity or torsion-freeness are still sensible and very natural concepts in our ordered setting.

Normally torsion-freeness of monomial ideals under monomial operators

2018 ◽  
Vol 46 (12) ◽  
pp. 5447-5459 ◽  
Author(s):  
Mirsadegh Sayedsadeghi ◽  
Mehrdad Nasernejad
Keyword(s):  
Monomial Ideals ◽  
Torsion Freeness

scholarly journals On weakly periodic-like rings and commutativity theorems

2006 ◽  
Vol 37 (4) ◽  
pp. 333-343 ◽  
Author(s):  
Abu-Khuzam Hazar ◽  
Howard E. Bell ◽  
Adil Yaqub
Keyword(s):  
Nilpotent Element ◽  
Commutativity Theorems ◽  
Torsion Freeness ◽  
Positive Integers

A ring $R$ is called periodic if, for every $x$ in $R$, there exist distinct positive integers $m$ and $n$ such that $x^m=x^n$. An element $x$ of $R$ is called potent if $x^k=x$ for some integer $k>1$. A ring $R$ is called weakly periodic if every $x$ in $R$ can be written in the form $x=a+b$ for some nilpotent element $a$ and some potent element $b$ in $R$. A ring $R$ is called weakly periodic-like if every element $x$ in $R$ which is not in the center $C$ of $R$ can be written in the form $x=a+b$, with $a$ nilpotent and $b$ potent. Some structure and commutativity theorems are established for weakly periodic-like rings $R$ satisfying certain torsion-freeness hypotheses along with conditions involving some elements being central.

STRONGLY TORSION FREE ACTS OVER MONOIDS

2013 ◽  
Vol 06 (03) ◽  
pp. 1350049 ◽  
Author(s):  
Abas Zare ◽  
Akbar Golchin ◽  
Hossein Mohammadzadeh
Keyword(s):  
Rees Factor ◽  
Torsion Freeness ◽  
Torsion Free

An act AS is called torsion free if for any a, b ∈ AS and for any right cancellable element c ∈ S the equality ac = bc implies a = b. In [M. Satyanarayana, Quasi- and weakly-injective S-system, Math. Nachr.71 (1976) 183–190], torsion freeness is considered in a much stronger sense which we call in this paper strong torsion freeness and will characterize monoids by this property of their (cyclic, monocyclic, Rees factor) acts.

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