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C(X): Something old and something new.

Authors :
Azarpanah, F.
Ghashghaei, E.
Ghoulipour, M.
Source :
Communications in Algebra; 2021, Vol. 49 Issue 1, p185-206, 22p
Publication Year :
2021

Abstract

The aim of this paper is twofold. Firstly, to give short proofs of the celebrated results of Rudd (1970), De Marco (1972), Brookshear (1977), Neville (1990), and Vechtomov (1996) with the help of some well-known results in ring theory. Secondly, to establish new algebraic characterizations for when C(X) is von Neumann regular, semihereditary, or a Bézout ring. The notions of the greatest common divisor and least common multiple in the ring C(X) are studied. Finally, the space X, for which every idempotent of the classical quotient ring of C(X) is actually an element of C(X) itself, is completely determined. [ABSTRACT FROM AUTHOR]

Subjects

Subjects :
QUOTIENT rings
RING theory

Details

Language :
English
ISSN :
00927872
Volume :
49
Issue :
1
Database :
Complementary Index
Journal :
Communications in Algebra
Publication Type :
Academic Journal
Accession number :
147859128
Full Text :
https://doi.org/10.1080/00927872.2020.1797070