On Segregated Rings and Algebras

1 February 1957

journal article
research article
Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal

Vol. 11, 1-7
https://doi.org/10.1017/s0027763000001896

Abstract

Segregated algebras have been nicely characterized by M. Ikeda [4]. In this paper §1, we consider segregated rings and study the structure of such rings in Theorems 1.1 and 1.2. In §2, we specialize to the case of segregated algebras of finite dimension over a field. Theorem 2.1 gives a new characterization of such algebras. Theorem 2.2 shows an interesting property of segregated algebras; two segregated algebras S and T, with radicals N and P respectively, are isomorphic if and only if S/N² and T/P² are isomorphic.

Keywords

SEGREGATED RINGS
SEGREGATED ALGEBRAS
STRUCTURE
ISOMORPHIC
NEW CHARACTERIZATION
FINITE DIMENSION
NICELY CHARACTERIZED
INTERESTING PROPERTY

This publication has 2 references indexed in Scilit:

On Absolutely Segregated Algebras
Nagoya Mathematical Journal, 1953
On the Cohomology Theory for Associative Algebras
Annals of Mathematics, 1946