We calculate the Brauer group of the four dimensional Hopf algebra H4 introduced by M. E. Sweedler. This Brauer group BM(k,H4, R0) is defined with respect to a (quasi-) triangular structure on H4,â€¦ (More)

Classical Buchberger theory is generalized to a new family of rings. The family includes all subalgebras of the polynomial algebra in one variable. Some subalgebras of polynomial algebras in severalâ€¦ (More)

The classical theory of GrÃ¶bner bases, as developed by Bruno Buchberger, can be expanded to utilize objects more general than term orders. Each term order on the polynomial ring k[x] produces aâ€¦ (More)

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, aâ€¦ (More)

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, aâ€¦ (More)

For an ideal or K-subalgebra E of K[X1, . . . , Xn], consider subfields k âŠ‚ K, where E is generated â€“ as ideal or K-subalgebra â€“ by polynomials in k[X1, . . . , Xn]. It is a standard result forâ€¦ (More)