Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...

Let R be a left pure semisimple ring such that there are no nonzero homomorphisms from preinjective modules to non-preinjective indecomposable modules in R-mod, and let W be the left key R-module; i.e., W is the direct sum of all non-isomorphic non-preinjective indecomposable direct summands of products of preinjective left R-modules. We show that if the module W is endofinite, then R is a ring...

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

We demonstrate a compact and efficient diode-end-pumped TEM>(00) laser with output power of 30 W for 48 W of incident pump power by use of two coated Nd:YVO> (4) crystals to form a thermally stabilized flat-flat cavity. In Q -switched operation 25 W of average power at a pulse-repetition rate of 100 kHz and ~0.9-mJ pulse energy at a pulse-repetition rate of 10 kHz were produced.

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

Let k be a commutative ring, H a faithfully flat Hopf algebra with bijective antipode, A a k-flat right H-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants B = A , and we study the semisimplicity of the category of relative Hopf modules.

This article summarizes the IEC compliant power rating procedure applied to a hybrid CPV/PV module of EyeCon technology which uses III-V four-junction CPV cells in combination with bifacial c-Si PV cells. The combined output both solar cell types at standard test conditions reached 342 W/m2, corresponds world record efficiency 34.2% for conversion reference AM1.5g spectrum. For first time, we p...

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.

PURPOSE To quantify the power-output demands of men's road-cycling stage racing using a direct measure of power output. METHODS Power-output data were collected from 207 races over 6 competition years on 31 Australian national male road cyclists. Subjects performed a maximal graded exercise test in the laboratory to determine maximum aerobic-power output, and bicycles were fitted with SRM pow...