Associative Algebras Admitting a Quasi-multiplicative Basis

作者：Calderon Martin A J

来源：Algebras and Representation Theory, 2014, 17(6): 1889-1900.

DOI：10.1007/s10468-014-9482-y

• Associative algebra
• Multiplicative basis
• Structure theory

A basis of an associative algebra over an arbitrary base field , is called multiplicative if for any i,jaI we have that for some kaI. The class of associative algebras admitting a multiplicative basis can be seen as a particular case of the more general class of associative algebras admitting a quasi-multiplicative basis. In the present paper we prove that if an associative algebra admits a quasi-multiplicative basis then it decomposes as the sum of well-described ideals admitting quasi-multiplicative bases plus (maybe) a certain linear subspace. Also the minimality of is characterized in terms of the quasi-multiplicative basis and it is shown that, under mild conditions, the above decomposition is actually the direct sum of the family of its minimal ideals admitting a quasi-multiplicative basis.

• 出版日期2014-12