ON MEDIAL Q-ALGEBRAS
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In this paper, we show that the mapping p(x) = 0 ¤ x is an endomorphism of a Q-algebra X, which induces a congruence relation “ ~ ” such that X/p is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X,then Ig is an ignorable ideal of X
Abstract
In this paper, we show that the mapping p(x) = 0 ¤ x is an endomorphism of a Q-algebra X, which induces a congruence relation “ ~ ” such that X/p is a medial Q-algebra. We also study some decompositions of ideals in Q-algebras and obtain equivalent conditions for closed ideals. Moreover, we show that if I is an ideal of a Q-algebra X,then Ig is an ignorable ideal of X
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