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We introduce, in this article, a partial order on quasi-morphic rings and investigate the behavior of regular elements in such rings. Further, the cleanness of regular elements in quasi-morphic rings having internal-cancelltion has been derived. [ABSTRACT FROM AUTHOR]

Tom Dieck introduced a commutative triangle whereby the exponential morphism from the Burnside functor to the unit functor is factorized through the real representation functor. Tornehave introduced a p-adic variant of the exponential morphism. His construction involves real representations that are not well defined up to isomorphism. To obtain a well defined commutative triangle, we introduce the orientation functor, a quotient of the real representation functor. [ABSTRACT FROM AUTHOR]

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]

If M and N are modules, the concept of semiregularity (and regularity) of hom ( M , N ) is defined and studied, and the connection with the relative direct injective- and direct projective-properties is established. The relationship of semiregularity to the Jacobson radical of hom ( M , N ), to the singular and cosingular ideals of hom ( M , N ), and to the notion of lying over or under a direct summand, is described, and the basic results in the module case are extended. Communicated by R. Wisbauer. [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]

After the proof of a not very known refinement of the Noether Normalization Theorem, we obtain two sharp degree bounds for the geometric degree of a dominating morphism of irreducible affine algebraic varieties and for the degree of the components of the inverse of an isomorphism of such varieties, generalizing by this way the well-known Gabber bound for automorphisms of affine spaces. [ABSTRACT FROM AUTHOR]

In this note,we answer a question of Hong et al. (2003) by proving that if a is a monomorphism of a reduced ring R , and R is a-skew Armendariz, then R is a-rigid. [ABSTRACT FROM AUTHOR]