• Title/Summary/Keyword: cozero complemented space

Search Result 1, Processing Time 0.014 seconds

WHEN IS C(X) AN EM-RING?

  • Abuosba, Emad;Atassi, Isaaf
    • Communications of the Korean Mathematical Society
    • /
    • v.37 no.1
    • /
    • pp.17-29
    • /
    • 2022
  • A commutative ring with unity R is called an EM-ring if for any finitely generated ideal I there exist a in R and a finitely generated ideal J with Ann(J) = 0 and I = aJ. In this article it is proved that C(X) is an EM-ring if and only if for each U ∈ Coz (X), and each g ∈ C* (U) there is V ∈ Coz (X) such that U ⊆ V, ${\bar{V}}=X$, and g is continuously extendable on V. Such a space is called an EM-space. It is shown that EM-spaces include a large class of spaces as F-spaces and cozero complemented spaces. It is proved among other results that X is an EM-space if and only if the Stone-Čech compactification of X is.