Arbitrary algebras with a multiplicative basis

作者：Calderon Martin Antonio J; Navarro Izquierdo Francisco J

来源：Linear Algebra and Its Applications, 2016, 498: 106-116.

DOI：10.1016/j.laa.2015.01.021

• Multiplicative basis
• Associative algebra
• Non-associative algebra
• Infinite dimensional algebra
• Structure theory

Let U be an algebra of arbitrary dimension, over an arbitrary base field F and in which any identity on the product is not supposed. A basis B = {e(i)}(i is an element of I) of U is called multiplicative if for any i, j is an element of I we have that e(i)e(j) is an element of F-ek for some k is an element of I. We show that if U admits a multiplicative basis then it decomposes as the direct sum U = circle plus(k) J(k) of well-described ideals admitting each one a multiplicative basis. Also the minimality of U is characterized in terms of the multiplicative basis and it is shown that, under a mild condition, the above direct sum is by means of the family of its minimal ideals admitting a multiplicative basis.

• 出版日期2016-6-1