On feckly polar rings

ÇALCI T., Chen H.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.18, no.2, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1142/s021949881950021x
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Feckly polar ring, strongly pi-regular ring, pseudopolar ring, matrix extension, PSEUDO DRAZIN INVERSE, ELEMENTS, SUM
  • Ankara University Affiliated: Yes

Abstract

In this paper, we introduce a new notion which lies properly between strong pi-regularity and pseudopolarity. A ring R is feckly polar if for any a is an element of R there exists e is an element of comm(2) (a) such that a - e is an element of U(R), e - e(2) is an element of J(R) and (ae)(n) is an element of J(R) for some n is an element of N. Many structure theorems are proved. Further, we investigate feck polarity for triangular matrix and matrix rings. The relations among strongly pi-regular rings, pseudopolar rings and feckly polar rings are also obtained.