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.

scholarly journals Commutativity theorems for rings and groups with constraints on commutators

1984 ◽  
Vol 7 (3) ◽  
pp. 513-517 ◽  
Author(s):  
Evagelos Psomopoulos
Keyword(s):  
Associative Ring ◽  
Commutativity Theorems ◽  
Torsion Freeness ◽  
Positive Integers ◽  
Torsion Free

Letn>1,m,t,sbe any positive integers, and letRbe an associative ring with identity. Supposext[xn,y]=[x,ym]ysfor allx,yinR. If, further,Risn-torsion free, thenRis commutativite. Ifn-torsion freeness ofRis replaced by “m,nare relatively prime,” thenRis still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true whent=s=0andm=n+1.

QUANTIZATION OF REDUCTIVE LIE ALGEBRAS: CONSTRUCTION AND UNIVERSALITY

1993 ◽  
Vol 05 (02) ◽  
pp. 363-415 ◽  
Author(s):  
P. TRUINI ◽  
V. S. VARADARAJAN
Keyword(s):  
Lie Algebras ◽  
Hopf Algebras ◽  
Algebra Structure ◽  
Universal Deformations ◽  
Irreducible Modules ◽  
Coalgebra Structure ◽  
Torsion Freeness ◽  
Deformed Algebras ◽  
And Algebra ◽  
Torsion Free

The present paper addresses the question of universality of the quantization of reductive Lie algebras. Quantization is viewed as a torsion free deformation depending upon several parameters which are treated formally and not as complex numbers. The coalgebra and algebra structures are shown to restrict very sharply the possibilities for the infinite series in the generators of the Cartan subalgebra. Under an Ansatz which can be viewed as requiring that the two Borel subalgebras are deformed as Hopf algebras we construct a multi-parameter quantization which has the required property of universality. We also show that such a quantization can be defined so that the algebra structure is the same as that of the standard one-parameter quantization, the remaining parameters being relegated to the coalgebra structure. We discuss an example in which only the latter parameters appear in the deformation. We then complete the study of the universal deformations by developing some aspects of the representation theory of the deformed algebras. Using this theory, especially the freeness of the irreducible modules, we prove the analogue of the Poincaré-Birkhoff-Witt theorem, and, as a consequence, the torsion freeness of the universal deformations.

On Flatness Properties of Torsion Free Right Rees Factor Acts

2006 ◽  
Vol 73 (3) ◽  
pp. 470-474
Author(s):  
Qiao Husheng ◽  
Wang Limin ◽  
Liu Zhongkui
Keyword(s):  
Rees Factor ◽  
Torsion Free

scholarly journals SUR LA TORSION DANS LA COHOMOLOGIE DES VARIÉTÉS DE SHIMURA DE KOTTWITZ-HARRIS-TAYLOR

2017 ◽  
Vol 18 (3) ◽  
pp. 499-517 ◽  
Author(s):  
Pascal Boyer
Keyword(s):  
Maximal Ideal ◽  
Cohomology Class ◽  
Hecke Algebra ◽  
Galois Representation ◽  
Local System ◽  
Shimura Varieties ◽  
Shimura Variety ◽  
Torsion Freeness ◽  
Satake Parameters ◽  
Torsion Free

(Torsion in the cohomology of Kottwitz–Harris–Taylor Shimura varieties) When the level at $l$ of a Shimura variety of Kottwitz–Harris–Taylor is not maximal, its cohomology with coefficients in a $\overline{\mathbb{Z}}_{l}$-local system isn’t in general torsion free. In order to prove torsion freeness results of the cohomology, we localize at a maximal ideal $\mathfrak{m}$ of the Hecke algebra. We then prove a result of torsion freeness resting either on $\mathfrak{m}$ itself or on the Galois representation $\overline{\unicode[STIX]{x1D70C}}_{\mathfrak{m}}$ associated to it. Concerning the torsion, in a rather restricted case than Caraiani and Scholze (« On the generic part of the cohomology of compact unitary Shimura varieties », Preprint, 2015), we prove that the torsion doesn’t give new Satake parameters systems by showing that each torsion cohomology class can be raised in the free part of the cohomology of a Igusa variety.

TORSION-FREENESS FOR RINGS WITH ZERO-DIVISORS

2004 ◽  
Vol 03 (03) ◽  
pp. 221-237 ◽  
Author(s):  
JOHN DAUNS ◽  
LASZLO FUCHS
Keyword(s):  
Finitely Generated ◽  
Free Ring ◽  
Equivalent Definition ◽  
Zero Divisors ◽  
Morita Invariant ◽  
Torsion Freeness ◽  
The Right ◽  
Torsion Free

A right R-module MR over any ring R with 1 is called torsion-free if it satisfies the equality [Formula: see text] for every r∈R. An equivalent definition was used by Hattori [11]. We establish various properties of this concept, and investigate rings (called torsion-free rings) all of whose right ideals are torsion-free. In a torsion-free ring, the right annihilators of elements are always idempotent flat right ideals. The right p.p. rings are characterized as torsion-free rings in which the right annihilators of elements are finitely generated. An example shows that torsion-freeness ness is not a Morita invariant. Several ring and module properties are proved, showing that, in several respects, torsion-freeness ness behaves like flatness. We exhibit examples to point out that the concept of torsion-freeness ness discussed here is different from other notions.

scholarly journals The computational complexity of torsion-freeness of finitely presented groups

1997 ◽  
Vol 56 (2) ◽  
pp. 273-277 ◽  
Author(s):  
Steffen Lempp
Keyword(s):  
Computational Complexity ◽  
Arithmetical Hierarchy ◽  
Finitely Presented Groups ◽  
Torsion Freeness ◽  
Finitely Presented ◽  
Torsion Free

We determine the complexity of torsion-freeness of finitely presented groups in Kleene's arithmetical hierarchy as -complete. This implies in particular that there is no effective listing of all torsion-free finitely presented groups, or of all non-torsion-free finitely presented groups.

Jordan k-Homomorphisms onto Completely Prime ΓN Rings

1970 ◽  
Vol 30 ◽  
pp. 32-40
Author(s):  
Sujoy Charaborty ◽  
Akhil Chandra Paul
Keyword(s):  
Torsion Free

By introducing the notions of k-homomorphism, anti-k-homomorphism and Jordan khomomorphism of Nobusawa Γ -rings, we establish some significant results related to these concepts. If M1 is a Nobusawa Γ1 -ring and M2 is a 2-torsion free completely prime Nobusawa Γ2 -ring, then we prove that every Jordan k-homomorphism θ of M1 onto M2 such that k(Γ1 ) = Γ2 is either a k-homomorphism or an anti-k-homomorphism. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 32-40 DOI: http://dx.doi.org/10.3329/ganit.v30i0.8500  

Derivations of differentially semiprime rings

2019 ◽  
Vol 12 (05) ◽  
pp. 1950079
Author(s):  
Ahmad Al Khalaf ◽  
Iman Taha ◽  
Orest D. Artemovych ◽  
Abdullah Aljouiiee
Keyword(s):  
Commutative Ring ◽  
Semiprime Ring ◽  
Prime Rings ◽  
Commutative Case ◽  
Lie Ring ◽  
Lie Rings ◽  
Semiprime Rings ◽  
Torsion Free

Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

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