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SOME CHARACTERIZATIONS OF SELF-SYMMETRIC RINGS WITH INVOLUTION

TitleSOME CHARACTERIZATIONS OF SELF-SYMMETRIC RINGS WITH INVOLUTION
Publication TypeJournal Article
Year of Publication2015
AuthorsBattle, G
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume9
Issue3
Start Page225
Pagination6
Date Published07/2015
Type of ArticleScientific article
ISSN1314-0744
Keywordsautomorphism, involution, nilpotent, self-symmetric
Abstract

I.N. Herstein as well as Susan Montgomery have defined and made many contributions to the algebraic structures of  a ring $R$ with involution *. An intrinsic algebraic subset of such a ring is the set of symmetric elements $S = \{a| a = a^*\}$.  A ring $R$ with involution * is self-symmetric provided all its nontrivial ideals are symmetric. This paper will show that all self-symmetric rings with involution * are MP3 (Moore-Penrose 3) rings. In addition, some attempts will be made to characterize the $n \times n$ matrix ring, $M_n(R)$ over a self-symmetric MP3 ring.

This paper is dedicated to the late Dr. Cleon Russell Yohe,
algebraist at Washington University in St. Louis.

 

Short TitleSOME CHARACTERIZATIONS OF...
Alternate JournalIeJPAM
Refereed DesignationRefereed
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