Journal article
A theorem on Noetherian hereditary rings
Pacific journal of mathematics, Vol.45(1), pp.35-41
03/01/1973
DOI: 10.2140/pjm.1973.45.35
Abstract
It is shown (Theorem 2) that a semi-prime, left noetherian, left hereditary, two-sided Goldie ring is right noetherian if and only if the right module (Q/R) ⊕ R contains a copy of every simple right R-module, where Q is the classical quotient ring of R. Theorem 5 gives several necessary and sufficient conditions for a semi-prime principal left ideal ring which is right Goldie to be a principal right ideal ring. Among these is that R/A must be artinian for every essential left ideal A. It is known that a two-sided noetherian semi-prime ring is principal on the left if and only if it is principal on the right. On the other hand, if one drops the ascending chain condition on the right side of R, examples are known of principal left ideal domains (p.1.i. domains) which are not right principal. But, if we require that they be right Ore as well, things may be better. © 1973 Pacific Journal of Mathematics.
Details
- Title: Subtitle
- A theorem on Noetherian hereditary rings
- Creators
- Victor CamilloJohn Cozzens
- Resource Type
- Journal article
- Publication Details
- Pacific journal of mathematics, Vol.45(1), pp.35-41
- DOI
- 10.2140/pjm.1973.45.35
- ISSN
- 0030-8730
- eISSN
- 1945-5844
- Language
- English
- Date published
- 03/01/1973
- Academic Unit
- Mathematics
- Record Identifier
- 9984241047002771
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