abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

Let T be a Noetherian ring and f a nonzerodivisor on T . We study concrete necessary and sufficient conditions for a module over R = T/(f) to be weakly liftable to T , in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over T we define the loci for certain properties: liftab...

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial generalization of the work of Skoruppa and Zagier. This lifting is also related with the Ikeda lifting.

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

A module M is said to belifting if, for anysubmodule N of M, there exists a direct summand X contained in such that N/X small M/X. satisfy the finite internal exchange propertyif, any and sum decomposition M=Lni=1Mi, M′i Mi (i= 1,2, . , n) M=X⊕(Lni=1M′i). In this paper, we first give characterizations forthe square hollow uniform be lifting (extending). addition, solve negatively question "Does...

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...

Abstract. Let (R,P) be a Noetherian unique factorization do-main (UFD) and M be a finitely generated R-module. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphi...

We consider a generalization of lifting modules relative to a class A of modules and a proper class E of short exact sequences of modules. These modules will be called E-A-lifting. We establish characterizations of modules with the property that every direct sum of copies of them is E-A-lifting. 2000 Mathematics Subject Classification: 16S90, 16D80.

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...