Showing papers in "Journal of Algebra in 1979"

TL;DR: The notion of right (A, B)-Hopf modules was introduced by as discussed by the authors to obtain many freeness or projectivity criteria for a hopf algebra over a field k and a Hopf subalgebra over B.

TL;DR: In this paper, a ring basis for the shuffle algebra Sh(V) of a vector space V over a field K was constructed and a computational method for the study of commutative pointed irreducible Hopf algebras was presented.

TL;DR: In this paper, the authors give a general foundation for the theory of quadratic and hermitian forms over rings with involution, and show how to solve a number of important classification problems of linear algebra.

TL;DR: The classical nullstellensatz theorem states that a reduced affine variety can be distinguished from its subschemes by its closed points with a bounded index of nilpotency as discussed by the authors.

TL;DR: In this article, the main concepts under study have been K,-categoricity, N,categoricality, and w-stability, which apply either to complete theories or to individual structures.

TL;DR: In this article, the cancellation problem was extended to equations F such that B is Galois over A, i.e., A and BC have the same quotient field, where G = Aut, B. In [9] and [7] th is was done for F = bTn + a with n > 1 and coprime with the characteristic of k.

TL;DR: In this paper, the determinant of the Gram matrix whose (i, j)th entry is (ei, ej) was evaluated and a lower bound on the p-modular irreducible degrees for the symmetric group 6,, for the results in [1] show that if pe exactly divides det p, then the pmodular representation of G arising from Su has dimension at least d e.

TL;DR: In this article, the authors studied the (n k)-order Pfaffians of an alternating matrix and proved that the height and depth of the ideal matrix are bounded by the number of entries in the matrix.

TL;DR: In this paper, the authors introduced the notion of a Z-form of the flag-algebra R[G/U] with generators and relations, given by the presentation, with the coefficients of these relations in Z, but also these relations generate, over Z, all relations on the (y,> with coefficients in Z).

TL;DR: In a beautiful but unpublished thesis written in 1972, Patton as discussed by the authors proved the corresponding results for all the groups SL(n, q), as well as for Sp(2m, q) with 2 odd.