摘要:

Varieties of Jordan pairs are considered in the present paper. The main results obtained are the following.1. The special Jordan pairs do not form a variety. More precisely, we give an example of a special Jordan pair and its homomorphic image being not special. 2. The varieties of Jordan pairs var (Mn,Mn) and var (Hn,Hn) are not special when n > 3 for Mnand Hnbeing n x n matrices and symmetric matrices, respectively. 3. Some description of the representations of the pair (Hn,Hn) is obtained

ISSN:0092-7872    

DOI:10.1080/00927879408824989

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

Extensions of simple modules for the finite Chevalley group G2(p) with p >13 are completely determined in this note.

ISSN:0092-7872    

DOI:10.1080/00927879408824990

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824991

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

For a group G, elements a and b are said to be inverse-conjugate if α is conjugate to b−1. We classify all finite groups in which every pair of elements of the same order is either conjugate or inverse-conjugate. The groups with this property are either small soluble groups, which are explicitly listed, or the groups L2;(7), M11, M23and Aut(Sz(8)).

ISSN:0092-7872    

DOI:10.1080/00927879408824992

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824993

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

It is not uncommon for rings to have Gabriel localizations which do not possess the unique rank (UR) property although the rings themselves do have UR. We show that if F is a Gabriel filter of right ideals on a ring R and RFis the corresponding Gabriel localization, then free RF−modules of ranks m and n are isomorphic if and only if some F-dense submodule of (R/Tf(R))mis isomorphic to some F-dense submodule of (R/TF(R))n, where TF(R) is the F-torsion ideal of R.

ISSN:0092-7872    

DOI:10.1080/00927879408824994

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The double annihilator of any element in the socle of a nondegenerate quadratic Jordan algebra coincides with the principal inner ideal generated by this element. Since the socle satisfies dec on principal inner ideals, it also satisfies ace on annihilators of principal inner ideals.

ISSN:0092-7872    

DOI:10.1080/00927879408824995

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

Let A be a *-algebra. An additive mapping E : A → A is called a Jordan *-derivation if E(X2) = E(x)x*+xE(x) holds, for all x 6 A. These mappings have been extensively studied in the last 6 years by Bresar, Semrl, Vukman and Zalar because they are closely connected with the problem of representability of quadratic functionals by sesquilinear forms. This study was, however, always in the setting of associative rings. In the present paper we study Jordan *-derivations on the Cayley-Dickson algebra of octonions, which is not associative. Our first main result is that every Jordan *-derivation on the octonion algebra is of the form E(x)=ax*-xa. In the terminology of earlier papers this means that every Jordan *-derivation on the octonion algebra is inner. This generalizes the known fact that Jordan *-derivations on complex and quaternion algebras are inner. Our second main result is a representation theorem for quadratic functionals on octonion modules. Its proof uses the result mentioned above on Jordan *-derivations.

ISSN:0092-7872    

DOI:10.1080/00927879408824996

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824997

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

For a moduleMfor various quotient modulesM/NofM, cardinality restrictions are placed on the number of generators of submodules ofM/N, and on the (infinite) Goldie dimensions ofM/N. The conditionsFGSandTCof R. Kurshan are formulated and generalized for arbitrary cardinals. The module theoretic consequences of these and other such finite-ness conditions with ascending chain conditions are explored.

ISSN:0092-7872    

DOI:10.1080/00927879408824998

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor