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C(X): Something old and something new.
- 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 :
- QUOTIENT rings
RING theory
Subjects
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