Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Order in a special class of rings and a structure theorem
HTML articles powered by AMS MathViewer

by Alexander Abian PDF
Proc. Amer. Math. Soc. 52 (1975), 45-49 Request permission

Addendum: Proc. Amer. Math. Soc. 61 (1976), 188.

Abstract:

Below a special class of not necessarily associative or commutative rings $A$ is considered which is characterized by the property that $A$ has no nonzero nilpotent element and that a product of elements of $A$ which is equal to zero remains equal to zero no matter how its factors are associated. It is shown that $(A, \leqslant )$ is a partially ordered set where $x \leqslant y$ if and only if $xy = {x^2}$. Also it is shown that $(A, \leqslant )$ is infinitely distributive, i.e., $r\sup {x_i} = \sup r{x_i}$. Finally, based on Zorn’s lemma it is shown that $A$ is isomorphic to a subdirect product of not necessarily associative or commutative rings without zero divisors.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17E05, 06A70
  • Retrieve articles in all journals with MSC: 17E05, 06A70
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 45-49
  • MSC: Primary 17E05; Secondary 06A70
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374222-8
  • MathSciNet review: 0374222