150 research outputs found
Tilting modules over valuation domains
No full textThe structure of tilting modules over valuation domains R is investigated. It is proved that the S-divisible modules introduced by Fuchs-Salce are canonical generators for the tilting
torsion classes over valuation domains, assuming V=L and that the cardinality of the pure-injective hull of R is at most the continuum when the tilting generator has uncountable rank
An indepedence result on cotorsion theories over valuation domains
No full textIt is shown that, over suitable valuation domains R with field of quotients Q, the cotorsion theory G(K) generated by K = Q/R coincides with the cotorsion theory Cr-partial derivative cogenerated by the Fuchs' divisible module partial derivative, provided that Godel's Axiom of Constructibility V = L is assumed. On the other hand, assuming Martin's Axiom and the negation of the Continuum Hypothesis, it is proved that the cotorsion theory G(K) is strictly smaller than C-partial derivative. by exhibiting a strongly (N - k )-free divisible module M of projective dimension 2 such that Ext(R)(1) (M, K) = 0. Applications to Whitehead R modules are derive
The Hierarchy of Uniserial Modules Over A Valuation Domain
No full textThe class of uniserial modules (i.e. modules whose submodules form a chain under inclusion) is studied over a valuation domain R. The isomorphy classes of torsion uniserial R-modules form a monoid Unis R under the operation Tor. In this paper, certain submonoids of Unis R are investigated, which consist of nonfinitely annihilated uniserials; these include all the nonstandard uniserial modules. Some of the submonoids turn out to be Clifford semigroups (i.e. unions of groups). Several results give information about the structure of monoids and about their group constituents. The non-finitely annihilated uniserials are classified into six classes; this classification is slightly different from the one for non-standard uniserials due to Bazzoni-Salce
Salce family
No full textL-R: Dorothy Curtis (later Trafton), Kathleen Curtis Salce, Virgilio Salce, others unidentified
Arthur Salce, Candelaria Gutierrez Salce, Florinda Gutierrez and Emil KAllina
No full textGroup standing on dirt road. L-R: Arthur Salce, Candelaria Gutierrez Salce, Florinda Gutierrez, Emil Kalina (in uniform
Vivian, Richard and Bertha Salce
No full textL-R: Vivian Salce, Richard Salce and Bertha Salce (children of Virgil (Virgilio) and Cathleen Curtis Salce) seated on hood of truc
Salce children and their children
No full textL-R: Ida Salce Gutierrez with her son James, Cathy in front of Ida; Lena Salce Apodaca with daughter Charlene; Dorothy Curtis (later Trafton), her mother Dulcelina (Dulce) Salce Curtis, Evelyn Curtis (later Losack); Cathleen Curtis Salce and Virgil Salce with children Bertha, Vivian and Richar
Elongations of Uniserial Modules Over Valuation Domains
No full textAbstractLet U and W be uniserial modules over a valuation domain. Existence and uniqueness of uniserial modules V such that there exists an exact sequence 0 → W → V → U → 0 are discussed. Complete answers are obtained for both standard and non-standard U
- …
