@article{(Open Science Index):https://publications.waset.org/pdf/10011913,
	  title     = {Integral Domains and Their Algebras: Topological Aspects},
	  author    = {Shai Sarussi},
	  country	= {},
	  institution	= {},
	  abstract     = {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.},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {15},
	  number    = {3},
	  year      = {2021},
	  pages     = {41 - 45},
	  ee        = {https://publications.waset.org/pdf/10011913},
	  url   	= {https://publications.waset.org/vol/171},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 171, 2021},
	}