Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings

Authors

  • M. A. Dokuchaev Univ. Sao Paulo, Brazil
  • V. V. Kirichenko

Abstract

We say that A is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) A -module U, the dual module U* is a simple left (right) A -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles.

Published

25.07.2002

Issue

Section

Research articles

How to Cite

Dokuchaev, M. A., and V. V. Kirichenko. “Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings”. Ukrains’kyi Matematychnyi Zhurnal, vol. 54, no. 7, July 2002, pp. 919-30, https://umj.imath.kiev.ua/index.php/umj/article/view/4128.