2004http://hdl.handle.net/123456789/242023-03-30T05:26:45Z2023-03-30T05:26:45ZCorrect classes of modulesWisbauer, Roberthttp://hdl.handle.net/123456789/1372020-01-24T21:27:11Z2004-01-01T00:00:00ZCorrect classes of modules
Wisbauer, Robert
For a ring R, call a class C of R-modules (pure-) mono-correct if for any M,N ∈ C the existence of (pure) monomorphisms M → N and N → M implies M ≃ N. Extending results and ideas of Rososhek from rings to modules, it is shown that, for an R-module M, the class [M] of all M-subgenerated modules is mono-correct if and only if M is semisimple, and the class of all weakly M-injective modules is mono-correct if and only if M is locally noetherian. Applying this to the functor ring of R-Mod provides a new proof that R is left pure semisimple if and only if R-Mod is pure-mono-correct. Furthermore, the class of pure-injective R-modules is always pure-mono-correct, and it is mono-correct if and only if R is von Neumann regular. The dual notion epi-correctness is also considered and it is shown that a ring R is left perfect if and only if the class of all flat R-modules is epi-correct. At the end some open problems are stated.
2004-01-01T00:00:00ZOn simple groups of large exponentsSonkin, Dmitriyhttp://hdl.handle.net/123456789/1362020-01-24T21:28:04Z2004-01-01T00:00:00ZOn simple groups of large exponents
Sonkin, Dmitriy
It is shown that the set of pairwise non-isomorphic 2-generated simple groups of exponent n (n ≥ 248 and n is odd or divisible by 29) is of cardinality continuum. As a corollary, for any
sufficiently large n the set of pairwise non-isomorphic 2-generated groups of exponent n is of cardinality continuum.
2004-01-01T00:00:00ZFinite groups with a system of generalized central elementsShemetkova, Olgahttp://hdl.handle.net/123456789/1352020-01-24T21:28:57Z2004-01-01T00:00:00ZFinite groups with a system of generalized central elements
Shemetkova, Olga
Let H be a normal subgroup of a finite group G. A number of authors have investigated the structure of G under the assumption that all minimal or maximal subgroups in Sylow
subgroups of H are well-situated in G. A general approach to the results of that kind is proposed in this article. The author has found the conditions for p-elements of H under which G-chief p-factors of H are F-central in G.
2004-01-01T00:00:00ZBasic semigroups: theory and applicationsPonizovskii, J. S.http://hdl.handle.net/123456789/1342020-01-24T21:26:41Z2004-01-01T00:00:00ZBasic semigroups: theory and applications
Ponizovskii, J. S.
A concept of basic matrix semigroups over fields (with some variations) is introduced and throughly investigated. Sections 1 and 2 contain main definitions, Section 3 treats some properties of basic semigroups, Section 4 is devoted to some application of basic semigroups: matrix representations (including faithful representations), finiteness theorems, the problem of Ko-rjakov (when a matrix semigroup over field K is conjugate to a matrix semigroup over a proper subfield of K). The paper is a survey and contains no proofs (which may be found in papers from References).
2004-01-01T00:00:00Z