Unitification of weakly Rickart and weakly p.q.-Baer *-rings

Year 2025, Volume: 37 Issue: 37, 179 - 189, 14.01.2025

Sanjay More Anil Khairnar B. N. Waphare

https://doi.org/10.24330/ieja.1518558

Abstract

S. K. Berberian raised the problem ``Can every weakly Rickart $*$-ring be embedded in a Rickart $*$-ring with preservation of right projections?". Berberian has given a partial solution to this problem. Khairnar and Waphare raised a similar problem for p.q.-Baer $*$-rings and gave a partial solution. In this paper, we give more general partial solutions to both the problems.

Keywords

Weakly Rickart $*$-ring, weakly p.q.-Baer $*$-ring, projection, central cover

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