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...

The proposed Java Module System (JAM) has two major deficiencies, as noted in our previous work: (a) its unintuitive class resolution can often give unexpected results; and (b) only a single instance of each module is permitted, which forces sharing of data and types, and so makes it difficult to reason about module invariants. Since JAM will be a part of Java 7, solving these problems before i...

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This paper presents a comparison between algebraic specii-cations-in-the-large and a type theoretical formulation of modular speci-cations, called deliverables. It is shown that the laws of module algebra can be translated to laws about deliverables which can be proved correct in type theory. The adequacy of the Extended Calculus of Constructions as a possible implementation of type theory is d...

In (2003), we proved the injective homotopy exact sequence of modules by a method that does not refer to any elements of the sets in the argument, so that the duality applies automatically in the projective homotopy theory (of modules) without further derivation. We inherit this fashion in this paper during our process of expanding the homotopy exact sequence. We name the resulting doubly infin...

Acknowledgements My deepest thanks go to Tim Römer for his guidance into mathematics and mathematical life since many years now, his support and encouragement during all that time. I wish to thank Winfried Bruns for his interest and many warm and refreshing conversations. I thank Christof and Jochen for always listening to my more or more often less exigent problems. I would also like to thank ...

Introduction. The notion of an additive category was abstracted from the example of all modules over a ring, a very large category. However with tongue firmly in cheek, one can define a ring with identity (all rings will have identity) as an additive category with just one object. Years ago, the notion of a Morita context was expounded with a certain amount of labour. A Morita context turned ou...

For this quarter of century, quantum differential operators in a lower dimensional submanifold embedded or immersed in real n-dimensional euclidean space E n have been studied as physical models, which are realized as restriction of the operators in E n to the submanifold. For this decade, the Dirac operators in the submanifold have been investigated, which are identified with operators of the ...

In this paper, the effect of the cell-temperature on the performance of photovoltaic (PV) module is evaluated. The evaluation is based on a mathematical module (single diode equivalent circuit) and practically based on solar module tester (SMT). Solara®130W PV crystalline silicon module was used in this simulation. The SMT is able to supply a constant irradiance level (1000W/m2) or any other de...

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α, β)higher derivation and demonstrate that a filter of a hereditary torsion theory that is invariant for α and β is (α, β)-higher derivation invariant. As a consequence, any higher derivation can be extended from a module to its module of quotients. Then...