Morita contexts and unitary ideals of rings; pp. 122–134

Proceedings of the Estonian Academy of Sciences

article

Kristo Väljako¹  Valdis Laan¹ 

[1] Institute of Mathematics and Statistics, University of Tartu

关键词: ring theory;    ring;    ideal;    bimodule;    quantale;    Morita context;   

DOI  :  10.3176/proc.2021.2.02

学科分类：内科医学

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

In this paper we study Morita contexts between rings without identity. We prove that if two associative rings are connected by a Morita context with surjective mappings, then these rings have isomorphic quantales of unitary ideals. We also show that the quotient rings by ideals that correspond to each other under that isomorphism are connected by a Morita context with surjective mappings. In addition, we consider how annihilators and two-sided socles behave under that isomorphism.

【 授权许可】

CC BY