Independence in Completions and Endomorphism Algebras.
In this paper, we deal with the study of intermediate domains between a domain and a domain such that is an intersection of localizations of , namely the pair . More precisely, we study the pair and the pair , where and . We prove that, if is a Jaffard domain, then is a Jaffard pair, which generalize [5, Théorème 1.9]. We also show that if is an -domain, then is a residually algebraic pair (that is for each intermediate domain between and , if is a prime ideal of ...
Quasi-injective modules over valuation domains are classified by means of complete sets of cardinal invariants.
We describe the isolated points of an arbitrary topological space . If the -specialization pre-order on has enough maximal elements, then a point is an isolated point in if and only if is both an isolated point in the subspaces of -kerneled points of and in the -closure of (a special case of this result is proved in Mehrvarz A.A., Samei K., On commutative Gelfand rings, J. Sci. Islam. Repub. Iran 10 (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime...