In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

We consider the assembly map for principal bundles with fiber a countable discrete group. obtain an index-theoretic interpretation of this homomorphism by providing tensor-product presentation module sections associated to Miščenko line bundle. In addition, we give proof Atiyah’s L2-index theorem in general context flat finitely generated projective Hilbert C∗-modules over compact Hausdorff spa...

The idempotent problem of a finitely generated inverse semi-group is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent problem is necessarily finite. This answers a question of Gilbert and Noonan Heale, and establishes a gen-eralisation to inverse semigroups of Anisimov's Th...

The author’s modification of Eilenberg theorem relates the so-called conjunctive varieties of regular languages with pseudovarieties of idempotent semirings. Recent results by Pastijn and his co-authors lead to the description of the lattice of all (pseudo)varieties of idempotent semirings with idempotent multiplication. We describe here the corresponding 78 varieties of languages.

An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempote...

Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of v...

We study H∗(P ), the mod p cohomology of a finite p–group P , viewed as an Fp[Out(P )]–module. In particular, we study the conjecture, first considered by Martino and Priddy, that, if eS ∈ Fp[Out(P )] is a primitive idempotent associated to an irreducible Fp[Out(P )]–module S, then the Krull dimension of eSH ∗(P ) equals the rank of P . The rank is an upper bound by Quillen’s work, and the conj...

Protected module architectures (PMA) are an isolation mechanism that emerging processors provide as security building blocks for modern software systems. Reasoning about these building blocks means reasoning about elaborate assembly code, which can be very complex due to the loose structure of the code. One way to overcome this complexity is providing the code with a well-structured semantics. ...