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...

In this note we study a certain formal group law over a complete discrete valuation ring F[[un−1]] of characteristic p > 0 which is of height n over the closed point and of height n− 1 over the generic point. By adjoining all coefficients of an isomorphism between the formal group law on the generic point and the Honda group law Hn−1 of height n − 1, we get a Galois extension of the quotient fi...

In this article, we present the structure of η-intuitionistic fuzzy ring. An ring is a which built with combinating definition ring, intuitionistic set, and set. The set characterized by any value η∈[0,1], where degree membership μ_(A^η ) (k) obtained based on averaging operator μ_A η∈[0,1]. While non ν_(A^η ν_A 1-η∈[0,1]. its development, new concepts were obtained, namely ideal properties rel...

We study the ideal generated by constant-term free B-quasisymmetric polynomials, and prove that the quotient of the polynomial ring by this ideal has dimension given by 1 2n+1 ` 3n

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohom...

Generic linkage is used to compute a prime ideal such that the radical of the initial ideal of the prime ideal is equal to the radical of a given codimension two monomial ideal that has a Cohen-Macaulay quotient ring.

The motivation for computing in a suitably chosen homomorphic image of the original problem domain is that the computation there is either easier or is possible, whereas in the original domain it was either harder or impossible. For example, any homomorphic image of the infinite ring of integers is a finite ring, and computation in a finite set is usually easier than in an infinite set; as we h...