They cover the construction of a

quotient ring of Z2F in which a binomial 1 + ?

Then [r.sub.p]([H.sub.n](1,q)) is isomorphic to the

quotient ring Z[x,y]/1.

4.4 The RSA on the

quotient ring of Gaussian integers

Hotta-Springer [11] and Garsia-Procesi [9] discovered that the cohomology ring of the Springer fiber indexed by a partition p of n is isomorphic to certain

quotient ring of F[X], which admits a graded [G.sub.n]-module structure corresponding to the modified Hall-Littlewood symmetric function [[??].sub.[mu]] (x; t) via the Frobenius characteristic map.

Throught this paper we will use the following notation: U will be the (two-sided) Utumi

quotient ring of a ring R (sometimes, as in [1], U is called the symmetric ring of quotients).

Throughout the paper unless specifically stated, R always denotes a prime ring with center Z(R) and extended centroid C, right Utumi

quotient ring U.

Throughout this paper, unless specially stated, R always denotes a prime ring with center Z(R), with extended centroid C, and with two-sided Martin- dale

quotient ring Q.

If S is a multiplicatively closed subset of R, then we may form the ring of quotients (or simply the

quotient ring when there is no chance of confusion),

They are orders in Artinian rings, Goldie's theorem, and the largest left

quotient ring of a ring; the invariant theory of Artin-Schelter regular algebras: a survey; the Catalan combinatorics of the hereditary Artin algebras; Grassmannians, flag varieties, and Gelfand-Zetlin polytopes; and on the combinatorics of the set of tilting modules.

Certain orbits of the reflection group action give a basis for the

quotient ring, from this they found a formula for the corresponding Littlewood-Richardson coefficients in their

quotient ring which was equal to a formula obtained by Kac [17] and Walton [30] for fusion coefficients in a Wess-Zumino-Witten conformal field theory.

Let R be a prime ring of characteristic [not equal to] 2 with right

quotient ring U and extended centroid C, g [not equal to] 0 a generalized derivation of R, L a non-central Lie ideal of R and n [greater than or equal to] 1 such that [g(u), u][.sup.n] = 0, for all u [member of] L.

Gordon, On the

quotient ring by diagonal coinvariants, Invent.