Embeddings of universal algebras into simple ones
The paper deals with the problem of the embeddability of algebras of a variety into simple algebras of the same variety by means of the concept of polynomial algebras. Two families of varieties are studied and the results obtained are presented in two theorems. The first theorem gives a sufficient condition of embeddability for the case of varieties of universal algebras which possess a nullary operation. A corollary applies this result to the case of groups in order to reprove the already known fact that every group is embeddable into a simple group. The second theorem gives a necessary and sufficient condition of embeddability for the case of varieties of multioperator groups. Again, a corollary applies this result to the case of rings in order to reprove that a ring R is embeddable into a simple ring if and only if the additive group \((R,+)\) is torsionfree or has as exponent a prime.
scientific article; zbMATH DE number 3869405