# SOME CHARACTERIZATIONS OF SELF-SYMMETRIC RINGS WITH INVOLUTION

 Title SOME CHARACTERIZATIONS OF SELF-SYMMETRIC RINGS WITH INVOLUTION Publication Type Journal Article Year of Publication 2015 Authors Battle, G Journal International Electronic Journal of Pure and Applied Mathematics Volume 9 Issue 3 Start Page 225 Pagination 6 Date Published 07/2015 Type of Article Scientific article ISSN 1314-0744 Keywords automorphism, 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 Title SOME CHARACTERIZATIONS OF... Alternate Journal IeJPAM Refereed Designation Refereed