DERIVABLE MAPS AND GENERALIZED DERIVATIONS

被引:4
作者
Pan, Zhidong [1 ]
机构
[1] Saginaw Valley State Univ, Dept Math, University Ctr, MI 48710 USA
来源
OPERATORS AND MATRICES | 2014年 / 8卷 / 04期
关键词
Derivable map; derivation; ALGEBRAS; HOMOMORPHISMS; MAPPINGS;
D O I
10.7153/oam-08-69
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let A be a unital algebra, M be an A -bimodule, L(A, M) be the set of all linear maps from A to M, and R-A be a relation on A. Amap d. L(A, M) is called derivable on R-A if delta(AB) = delta(A) B+A delta (B) for all (A, B) is an element of R-A. One purpose of this paper is to propose the study of derivable maps on a new, but natural, relation R-A. Moreover, we give a characterization of generalized derivations on M-n(C), the nxn matrix algebra over the complex numbers; specifically, a linear map delta on M-n(C) is a generalized derivation iff there exists an M is an element of M-n (C) such that delta (AB) = delta (A) B+ A delta (B), for all A, B is an element of M-n (C) satisfying AMB = 0; in this case delta(I) = cM, for some c is an element of C.
引用
收藏
页码:1191 / 1199
页数:9
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