This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.
We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...
Let be finite dimensional -algebra which is a complete intersection, i.e. whith a regular sequences . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra is solvable. We prove this in case is in addition graded and generated by elements of degree 1.
Sia un anello di caratteristica diseguale. Si stabiliscono formule generali per gli endomorfismi di una differenziazione o -iterativa di , con non zerodivisore di R. Tali formule sono note nel caso della caratteristica eguale.
We consider a commutative ring with identity and a positive integer . We characterize all the 3-tuples of linear transforms over , having the “circular convolution” property, i.eṡuch that for all .
In this paper, we give new characterizations of the --Bézout property of trivial ring extensions. Also, we investigate the transfer of this property to homomorphic images and to finite direct products. Our results generate original examples which enrich the current literature with new examples of non--Bézout --Bézout rings and examples of non--Bézout --Bézout rings.