Finite dimensional zero product determined algebras are generated by idempotents

被引：13
|
作者：
Bresar, Matej [1 ,2 ]
机构：
[1] Univ Ljubljana, Fac Math & Phys, Ljubljana 61000, Slovenia
[2] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
来源：
EXPOSITIONES MATHEMATICAE | 2016年 / 34卷 / 01期
关键词：
Zero product determined algebra; Finite dimensional algebra; Idempotent; C-ASTERISK-ALGEBRAS; NILPOTENT ELEMENTS; MATRIX ALGEBRAS; BANACH-ALGEBRAS; DERIVATIONS; MAPS; RINGS; HYPERREFLEXIVITY; XY;
D O I：
10.1016/j.exmath.2015.07.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An algebra A is said to be zero product determined if every bilinear map f from A x A into an arbitrary vector space X with the property that f (x, y) = 0 whenever xy = 0 is of the form f (x, y) =.(xy) for some linear map : A -> X. It is known, and easy to see, that an algebra generated by idempotents is zero product determined. The main new result of this partially expository paper states that for finite dimensional (unital) algebras the converse is also true. Thus, if such an algebra is zero product determined, then it is generated by idempotents. (C) 2015 Elsevier GmbH. All rights reserved.
引用
收藏
页码：130 / 143
页数：14
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