Pseudo-reflection group actions on local rings

Cyclic Group Actions on Polynomial Rings

We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...

Pseudo-Valuation ‏‎Near ‎ring‎ and Pseudo-Valuation N-group in Near Rings

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

Pseudo-almost valuation rings

The aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎It is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

Group Actions on Polynomial and Power Series Rings

The Flag Major Index and Group Actions on Polynomial Rings

A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type B, it is equidistributed with length. For more general wreath products it appears in an explicit formula for the Hilbert series of the (diagonal action) invariant algebra.