Results 211 to 220 of about 8,162 (244)

The ring as a torsion-free cover

Israel Journal of Mathematics, 1980
LetR be an integral domain andI a non-zero ideal ofR. The canonical mapR→R/I is called atorsion-free cover ofR/I if everyR-homomorphism from a torsion-freeR-module intoR/I can be factored throughR. The main result of this paper is thatR→R/I is a torsion-free cover if and only ifR is complete in theR-topology andI is an ideal of injective dimension 1 ...
openaire   +2 more sources

Semiprime torsion free rings

Mathematical Journal of Okayama University, 1995
In an earlier paper, the author developed a theory that in a semiprime torsion free ring, there is an essential direct sum of three completely unique and algebraically very different types of ideals, one of which is discrete and the others are continuous.
openaire   +3 more sources

Commutativity of n-Torsion-Free Rings With Commuting Powers

Results in Mathematics, 1988
Let R be an associative ring satisfying the identity \(x^ ny^ n=y^ nx^ n\) and for any \(x\in R\), \(x\in Rx\cap xR\). The authors prove that R is commutative if one of the following conditions holds in R: i) \(n[x,y]=0\) implies \([x,y]=0\) and for any x,y\(\in R\) there exists a positive integer \(m=m(x,y)\) such that \((m,n)=1\), \([x,[x,(xy)^ m]]=0\
Janjić, Milan, Psomopoulos, Evagelos
openaire   +2 more sources

A Note on Group Rings of Certain Torsion-Free Groups

Canadian Mathematical Bulletin, 1972
AbstractAs a step towards characterizing ID-groups (i.e., groups G such that, for every ring R without zero-divisors, the group ring RG has no zero-divisors), Rudin and Schneider defined Ω-groups, a possibly wider class than that of right-orderable groups, and proved that if every non-trivial finitely generated subgroup of a group G has a non-trivial H-
Burns, R. G., Hale, V. W. D.
openaire   +2 more sources

Some torsion-free subgroups in group rings

Mathematical Journal of Okayama University, 1993
Let \(G\) be an arbitrary group and let \(R\) be a commutative ring with identity. Denote by \(\Delta_R(G)\) the augmentation ideal of the group algebra \(RG\). Given a normal subgroup \(N\) of \(G\), let \(\Delta_R(G,N)\) be the kernel of the natural homomorphism \(RG\to R(G/N)\).
openaire   +3 more sources

A remark on torsion-free subgroups in group rings

Mathematical Journal of Okayama University, 1996
Let \(R\) be an integral domain of characteristic \(0\) and \(G\) be a group. For any normal subgroup \(M\) of \(G\) denote by \(\Delta_R(G,M)\) the kernel of the natural homomorphism from \(RG\) to \(RG/M\). For any group \(M\) let \(TM\) be the set of torsion elements in \(M\).
openaire   +3 more sources

RADICALS OF ENDOMORPHISM RINGS OF TORSION-FREE ABELIAN GROUPS

Mathematics of the USSR-Sbornik, 1974
This paper deals with questions related to the nil radical and the Jacobson radical of the endomorphism rings of torsion-free abelian groups. The most complete results are obtained for groups of finite rank. A characterization is given for the Jacobson radical of the endomorphism ring of a torsion-free abelian group of finite rank. The question of when
openaire   +2 more sources

Torsion-free abelian groups with hereditary rings of endomorphisms

Algebra and Logic, 1988
Let S be an associative ring with 1, A be a unitary right S-module, A is said to be self-small, if the image of any homomorphism \(A\to \sum^{\oplus}_{i\in {\mathfrak M}}A_ i\), \(A_ i\cong A\), \(i\in {\mathfrak M}\) is contained in the sum of a finite number \(A_ i\) for any set \({\mathfrak M}\). An S-module G is said to be A-free (A-projective) if \
openaire   +1 more source

TORSION-FREE RINGS WITH FINITE AUTOMORPHISM GROUPS

Communications in Algebra, 2001
The paper considers finite rank torsion-free rings, i.e, subrings of finite-dimensional rational algebras. The main result of the paper is the characterization of finite rank torsion-free rings with finite automorphism groups. Nontrivial examples of rings R with AutR finite have been constructed.
openaire   +1 more source

The Ring of Endomorphisms of a Torsion-Free Module

Journal of the London Mathematical Society, 1964
Feller, E. H., Swokowski, E. W.
openaire   +1 more source