Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible...

We prove that every perfect torsion theory for a ring R is differential (in the sense of [2]). In this case, we construct the extension of a derivation of a right R-module M to a derivation of the module of quotients of M . Then, we prove that the Lambek and Goldie torsion theories for any R are differential.

For σ−PWB extensions, we extend to modules the theory of Gröbner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative σ − PWB extension, we compute the module of syzygies of a submodule of the free module A.

Let S be an unramified regular local ring having mixed characteristic p > 0 and R the integral closure of S in a pth root extension of its quotient field. We show that R admits a finite, birational module M such that depth(M) = dim(R). In other words, R admits a maximal Cohen-Macaulay module.

This paper is prompted by work of Grandjee an and Ladra on homol-ogy crossed modules. We deene the homology of a crossed module in dimensions one and two via the equivalence of categories with group objects in groupoids. We show that for any perfect crossed module, its second homology crossed module occurs as the kernel of its universal central extension as deened by Norrie. Our rst homology is...

This paper describes about information extraction system, which is an extension of the system developed by team Hitachi for "Disease/Disorder Template filling” task organized by ShARe/CLEF eHealth Evolution Lab 2014. In this extension module we focus on extraction of numerical attributes and values from discharge summary records and associating correct relation between attributes and values. We...

We present the programming language Keris, an extension of Java with explicit support for software evolution. Keris introduces extensible modules as the basic building blocks for software. Modules are composed hierarchically revealing explicitly the architecture of systems. A distinct feature of the module design is that modules do not get linked manually. Instead, the wiring of modules gets in...

In this paper we give characterizations of essential left ideals of a C*-algebra A in terms of their properties as operator A-modules. Conversely, we seek C*-algebraic characterizations of those ideals J in A such that A is an essential extension of J in various categories of operator modules. In the case of two-sided ideals, we prove that all the above concepts coincide. We obtain results, ana...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

Detailed analysis of the modular Type I polyketide synthase (PKS) involved in the biosynthesis of the marginolactone azalomycin F in mangrove Streptomyces sp. 211726 has shown that only nineteen extension modules are required to accomplish twenty cycles of polyketide chain elongation. Analysis of the products of a PKS mutant specifically inactivated in the dehydratase domain of extension-module...