Embeddings of universal algebras into simple ones
type: Item
instance of: scholarly article
title: Embeddings of universal algebras into simple ones
zbMATH Open document ID: 0546.08002
DOI: 10.1007/BF01191495
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08B99
zbMATH DE Number: 3869405
zbMATH Keywords: embeddability of algebras
zbMATH Keywords: simple algebras
zbMATH Keywords: polynomial algebras
zbMATH Keywords: varieties of multioperator groups
author: Gerhard Kowol
reviewed by: Dorel Lucanu
MaRDI profile type: Publication
cites work: Q5509022
cites work: On a class of simple rings
cites work: On the embedding of a group in a join of given groups
cites work: Groups with Multiple Operators
cites work: Embedding Theorems for Groups
cites work: The equation 𝑥’≡𝑥𝑑-𝑑𝑥=𝑏
cites work: Q3236717
cites work: Approximation durch Polynomfunktionen auf universellen Algebren
cites work: Embedding Non-Associative Rings in Division Rings
cites work: A Note on Algebraically Closed Groups
description: scientific article; zbMATH DE number 3869405