Module algebra is described as a parametrised data type that takes a three sorted parameter, involving signatures, renamings and atomic specifications. An actual parameter describing relational specifications is given and a biinterpretation model is made for the resulting specification. 1986 CR Categories: D.2.0 [software engineering]: requirements/ specificationslanguages; D.2.2 [software engi...

We present the coupling of atomic force microscopy (AFM) and nuclear magnetic resonance (NMR) technologies to enable topographical, mechanical, and chemical profiling of biological samples. Here, we fabricate and perform proof-of-concept testing of radiofrequency planar microcoils on commercial AFM cantilevers. The sensitive region of the coil was estimated to cover an approximate volume of 19....

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

A program for computing pure angular momentum coefficients in relativistic atomic structure for any scalar one– and two–particle operator is presented. The program, written in Fortran 90/95 and based on techniques of second quantization, irreducible tensorial operators, quasispin and the theory of angular momentum, is intended to replace existing angular coefficient modules from GRASP92. The ne...

Let X be a compact Hausdorff space, and let {Ax : x ∈ X} {Bx collections of Banach algebras such that each Ax is Bx-bimodule. Using the theory bundles spaces as tool, we investigate module amenability certain Ax-valued functions on over Bx-valued X.

Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

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...