%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 Algebras over an Integral Domain and Immediate Neighbors
	%U https://publications.waset.org/pdf/10011915
	%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. A characterization of the property of immediate neighbors in
an Alexandroff topological space is given, in terms of closed and open
subsets of appropriate subspaces. Moreover, two special subspaces of
W are introduced, and a way in which their closed and open subsets
induce W is presented.
	%P 46 - 50