%0 Journal Article
	%A Shai Sarussi
	%D 2021
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 171, 2021
	%T Integral Domains and Their Algebras: Topological Aspects
	%U https://publications.waset.org/pdf/10011913
	%V 171
	%X Let S be an integral domain with field of fractions F
and let A be an F-algebra. An S-subalgebra R of A is called S-nice
if R∩F = S and the localization of R with respect to S \{0} is A.
Denoting by W the set of all S-nice subalgebras of A, and defining
a notion of open sets on W, one can view W as a T0-Alexandroff
space. Thus, the algebraic structure of W can be viewed from the
point of view of topology. It is shown that every nonempty open
subset of W has a maximal element in it, which is also a maximal
element of W. Moreover, a supremum of an irreducible subset of
W always exists. As a notable connection with valuation theory, one
considers the case in which S is a valuation domain and A is an
algebraic field extension of F; if S is indecomposed in A, then W is
an irreducible topological space, and W contains a greatest element.
	%P 41 - 45