Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.

Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

Abstract We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both non-associative and the classical theorem for associative Ore extensions. Along way, we develop hom-module theory. conclude with some examples extensions are all noetherian by our theorem.

In modeling studies or memory based on neural networks, both the selective enhancement and depression or synaptic strengths are required ror effident storage or inrormation (Sejnowski, 1977a,b; Kohonen, 1984; Bienenstock et aI, 1982; Sejnowski and Tesauro, 1989). We have tested this assumption in the hippocampus, a cortical structure or the brain that is involved in long-term memory. A brier, h...