The coinvariant algebra is a quotient of the polynomial ring Q[x1,…,xn] whose algebraic properties are governed by combinatorics permutations length n. A word w=w1…wn over positive integers packed if whenever i>2 appears as letter w, so does i−1. We introduce Sn which words. relate our to generalized rings Haglund, Rhoades, and Shimozono well superspace ring.

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

We develop the K-theory of sets with an action a pointed monoid (or scheme), analogous to modules over ring scheme). In order form localization sequences, we construct quotient category nice regular by Serre subcategory.

The role of symmetry in ring theory is universally recognized. most directly definable universal relation a symmetric set isomorphism. This article develops certain structure bipolar fuzzy subrings, including quotient ring, homomorphism, and We define (?,?)-cut investigate the algebraic attributions this phenomenon. also support prove various important properties relating to concept. Additional...

We give a general construction of rings graded by the conjugacy classes of a finite group. Some examples of our construction are the Hochschild cohomology ring of a finite group algebra, the Grothendieck ring of the Drinfel’d double of a group, and the orbifold cohomology ring for a global quotient. We generalize the first two examples by deriving product formulas for the Hochschild cohomology ...

The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

We define and study the Burnside quotient Green ring of a Mackey functor, introduced in our MSRI preprint [16]. Some refinements of Dress induction theory are presented, together with applications to computation results for K-theory and L-theory of finite and infinite groups.

We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[Z1 xn, y1,.. . , yn] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = { x 1 , . . . , xn} is classical. Introducing the second set of variables leads to a ring about which li...