Abstract. Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded...

Every ring extension of A by R induces a pair of group homomorphisms L : R → EndZ(A)/L(A);R : R → EndZ(A)/R(A), preserving multiplication, satisfying some certain conditions. A such 4-tuple (R,A,L,R) is called a ring pre-extension. Each ring pre-extension induces a R-bimodule structure on bicenter KA of ring A, and induces an obstruction k, which is a 3-cocycle of Z-algebra R, with coefficients...

I referred her to [2], where Theorem 3.6 asserts that K1(R) is R /Ẽ, where Ẽ is the group generated by (1 + xy)/(1 + yx) with x, y in R and 1 + xy in R and where the last sentence in §3 says that Ẽ is not [R, R] in the case when R = M2(Z/2Z) is the ring of 2 by 2 matrices over a field of two elements (Z is the ring of integers). Moreover, in this case the group K1(R) is trivial while R/[R , R] ...

In this paper we study codes where the alphabet is a finite Frobenius bimodule over a finite ring. We discuss the extension property for various weight functions. Employing an entirely character-theoretic approach and a duality theory for partitions on Frobenius bimodules we derive alternative proofs for the facts that the Hamming weight and the homogeneous weight satisfy the extension property...