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Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that E x t R ( G , G ) = 0 . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which are larger...

Almost perfect domains

S. Bazzoni, L. Salce (2003)

Colloquium Mathematicae

Commutative rings all of whose quotients over non-zero ideals are perfect rings are called almost perfect. Revisiting a paper by J. R. Smith on local domains with TTN, some basic results on these domains and their modules are obtained. Various examples of local almost perfect domains with different features are exhibited.

Almost Prüfer v-multiplication domains and the ring D + X D S [ X ]

Qing Li (2010)

Colloquium Mathematicae

This paper is a continuation of the investigation of almost Prüfer v-multiplication domains (APVMDs) begun by Li [Algebra Colloq., to appear]. We show that an integral domain D is an APVMD if and only if D is a locally APVMD and D is well behaved. We also prove that D is an APVMD if and only if the integral closure D̅ of D is a PVMD, D ⊆ D̅ is a root extension and D is t-linked under D̅. We introduce the notion of an almost t-splitting set. D ( S ) denotes the ring D + X D S [ X ] , where S is a multiplicatively closed...

Almost Q -rings

C. Jayaram (2004)

Archivum Mathematicum

In this paper we establish some new characterizations for Q -rings and Noetherian Q -rings.

Almost π -lattices

C. Jayaram (2004)

Czechoslovak Mathematical Journal

In this paper we establish some conditions for an almost π -domain to be a π -domain. Next π -lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for π -rings.

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