Pinched Veronese rings are formed by removing an algebra generator from a subring of polynomial ring. We study the homological properties such rings, including Cohen-Macaulay, Gorenstein, and complete intersection properties. Greco Martino classified Cohen-Macaulayness pinched maximum entry exponent vector monomial; we re-prove their results with semigroup methods correct omission small class e...

A function [Formula: see text], where text] is a commutative ring with unit element, called polyfunction if it admits polynomial representative text]. Based on this notion, we introduce invariants which associate to the numbers and subring generated by For invariant coincides number theoretic Smarandache or Kempner If every in polyfunction, then finite field according Rédei–Szele theorem, holds...

Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only the universally finite module differentials $\Omega_R$ a torsion-free $R$-module. We give new cases this conjecture by extending works G\"uttes (Arch Math 54:499-510, 1990) Corti\~na...

We use quivers and their representations to bring new perspectives on the subregular J-ring JC of a Coxeter system (W,S), subring Lusztig's J-ring. prove that is isomorphic suitable quotient path algebra double quiver (W,S). Up Morita equivalence, such quotients include group algebras all free products finite cyclic groups. then study category mod-AK dimensional right modules AK=K⊗ZJC over an a...

We suggest a new combinatorial construction for the cohomology ring of the ag manifold. The degree 2 commutation relations satissed by the divided diierence operators corresponding to positive roots deene a quadratic associative algebra. In this algebra, the formal analogues of Dunkl operators generate a commuta-tive subring, which is shown to be canonically isomorphic to the cohomology of the ...

Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...

Following the definition of quantum differential operators given in [LR1], we show that the ring of quantum differential operators on the affine line is the ring generated by x and ∂, the familiar differential operators on the line, along with two additional operators which we call ∂ 1 and ∂ −1 . We describe this ring both as a subring of the ring of graded endomorphisms and as a ring given by ...

This paper shows that certain primitive factor rings of U(sl(2,C)) embed in the rings of differential operators 9 on the curves yz =x “+I There is an action of SL(2,C) as automorphisms . of a making %i a (sl(2) x s1(2),SL(2)) Harish-Chandra bimodule in such a way that the invariant subring under the centre of SL(2), @, i s the primitive factor of U(sl(2)). This result describes all the Dixmier ...

We show that every quasi-ordinary Weierstrass polynomial P (Z) = Z + a1(X)Z d−1 + · · ·+ ad(X) ∈ K[[X]][Z], X = (X1, . . . , Xn), over an algebraically closed field of characterisic zero K, such that a1 = 0, is ν-quasi-ordinary. That means that if the discriminant ∆P ∈ K[[X]] is equal to a monomial times a unit then the ideal (a i (X))i=2,...,d is monomial and generated by one of a i (X). We us...

Lewin has proved that if S is a ring and R a subring of finite index in S, then R contains an ideal of S which is also of finite index; and Feigelstock has recently shown that other classes of subrings must contain ideals belonging to the same class. We provide some extensions of these results, and apply them to prime rings. In the final section, we investigate finiteness of rings having only f...