A well-known result of the theory of rings of quotients asserts that the essential ideals of a
semiprime associative algebra are themselves semiprime algebras and memorize both the …

In this paper we shall develop a structure theory for multiplicatively semiprime algebras. To
this end we shall introduce an algebraic closure for ideals of an algebra A, which involves …

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Let A be a semiprime associative algebra with an involution over a field of characteristic not
2, let K be the Lie algebra of all skew elements of A, and let Z [K, K] denote the annihilator of …

In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with
the corresponding well-known concept in the associative case. Specifically, we completely …

Algebra extensions A⊆ B where A is a left B-module such that the B-action extends the
multiplication in A are ubiquitous. We encounter examples of such extensions in the study of …

Applications of multiplication algebras to the algebraic and analytic strengthenings of
primeness and semiprimeness of (possibly non-associative) algebras are fully surveyed …

π-complemented algebras are defined as those (not necessarily associative or unital)
algebras such that each annihilator ideal is complemented by other annihilator ideal. For a …

For a nonassociative algebra A, by considering A as a left module over its multiplication
algebra M (A), a closure operation (termed the ε-closure) appears on the lattice IA of all …

Let A be an algebra whose multiplication algebra M (A) is semiprime. We prove that, except
in an exceptional case, the proper closed prime ideals of A are the maximal closed ideals of …