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For a class L of right modules we investigate the relations of monomorphic L-envelopes and epimorphic L-covers over pullback-pushout diagrams, and obtain some isomorphism equations between the envelopes of covers and the covers of envelopes. [ABSTRACT FROM AUTHOR]

In this paper we classify, up to exact isomorphism, the algebras in the title which contain a faithful element and in which every non-trivial table subset has dimension at least five. [ABSTRACT FROM AUTHOR]

Let D be a Prüfer domain, and denote by ± b ℑ( D ) the multiplicative group of all invertible fractional ideals of D , ordered by A ≤ B if and only if A ⊇ B . Denote by G i the value group of the valuation associated with the valuation ring D M i , where { M i } i ∈ I is the collection of all maximal ideals of D . In this note we prove that the natural map from ± b ℑ( D ) into ± b ∏ i ∈ I G i is an isomorphism onto the cardinal sum ± b ∐ i ∈ I G i if and only if D is h -local. As a corollary, the group of divisibility of an h -local Bézout domain is isomorphic to ± b ∐ i ∈ I G i , the notation being as above. [ABSTRACT FROM AUTHOR]