Several of the fundamental theorems about algebraic K, and Kr are concerned with finding unimodular elements, that is, elements of a projective module which generate a free summand. In this paper we use the notion of a basic element (in the terminology of Swan [22]) to extend these theorems to the context of finitely generated modules. Our techniques allow a simplification and strengthening of ...

Tripal is an open-source database platform primarily used for development of genomic, genetic and breeding databases. We report here on the release of the Chado Loader, Chado Data Display and Chado Search modules to extend the functionality of the core Tripal modules. These new extension modules provide additional tools for (1) data loading, (2) customized visualization and (3) advanced search ...

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

We introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of Rees algebras of modules, and to bound the length of normalization processes. In the case of regular base rings, the bounds are expressed in terms of Buchsbaum–Rim multiplicities and a module version of Briançon–Skoda numbers. Normalization of modules is the study of the i...

We will say that an alphabet A satisfies the extension property with respect to a weight w if every linear isomorphism between two linear codes in A that preserves w extends to a monomial transformation of A. In the 1960s MacWilliams proved that finite fields have the extension property with respect to Hamming weight. It is known that a module A has the extension property with respect to Hammin...

$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.

We prove a local monodromy theorem for p-adic differential equations on an annulus, answering a question of R. Crew. Specifically, suppose given a finite free module over the Robba ring (the ring of germs of functions analytic on some open p-adic annulus with outer radius 1) with a connection and a compatible Frobenius structure. We prove that the module admits a basis over a finite extension o...

A Hybrid Intelligent Architecture that aims to exploit the complementary features of expert systems and connectionist architecture, is proposed to revise input characterization and initial domain knowledge. HIA has two building blocks, a Rule-Based module and a Connectionist Architecture module. A speciic format for the rule-based description of the initial theory acquired from the application ...