This paper settles a problem raised at the end of the seventies by J.L. Alperin [Al1], E.C. Dade [Da] and J.F. Carlson [Ca1], namely the classification of torsion endo-trivial modules for a finite p-group over a field of characteristic p. Our results also imply, at least when p is odd, the complete classification of torsion endo-permutation modules. We refer to [CaTh] and [BoTh] for an overview...

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible times a nonempty product radical ideals. More precisely, investigate stability these properties under homomorphic image and their transfer to various contexts constructions such direct product, trivial ring extension amalgamated duplication along ideal. Our results generate exampl...

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

Owing to rising intentional events, supply chain disruptions have been considered by setting up a game between two players, namely, a designer and an interdictor contesting on minimizing and maximizing total cost, respectively. The previous studies have found the equilibrium solution by taking transportation, penalty and restoration cost into account. To contribute further, we examine how incor...

We investigate a strong version of the integral Tate conjecture for 1-cycles on product curve and surface over finite field, under assumption that is geometrically $$CH_0$$ -trivial. By this we mean any algebraically closed field extension, degree map zero-dimensional Chow group an isomorphism. This applies to Enriques surfaces. When Néron-Severi has no torsion, recover earlier results A. Pirut...

The external validity of artificial "trivial" laboratory settings is examined. Past views emphasizing generalizability of relations among conceptual variables are reviewed and affirmed, One major implication of typical challenges to the external validity of l ratory arch t ed wi h gression r search: If l borat ry es a ch ow n external validity, then laboratory studies should fail to detect rela...

In papers by Semmes [6], Macpherson and Neumann [4] and Brazil, Covington, Penttila, Praeger and Woods [2], it has been shown that stabilizers of filters (equivalently, stabilizers of ideals) play a crucial role in the study of maximal subgroups of infinite symmetric groups. Semmes proved that if if is a maximal subgroup of S = Sym (Q), where Q is a set of infinite cardinality K and H contains ...

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...

1 Rational Geometric Fundamental Groups Let K be a nitely generated eld with separable closure K s and absolute Galois group G K : By a curve C=K we always understand a smooth geometrically irreducible projective curve. Let F(C) be its function eld and let (C) be the Galois group of the maximal unramiied extension of F(C): We have the exact sequence 1 ! g (C) ! (C) ! G K ! 1 (?) where g (C) is ...