We define the concept of regularity for bigraded modules over a bigraded polynomial ring. In this setting we prove analogs of some of the classical results on m-regularity for graded modules over polynomial algebras.

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ⊗̂-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuou...

In this paper we prove analogs for the case of bigraded polynomial rings of theorems about regularity and saturation of ideals in simply graded polynomial rings.

In this paper, we classify $(q,q)$ -biprojective almost perfect nonlinear (APN) functions over notation="LaTeX">$\mathbb {L}\times \mathbb {L}$ under the natural left and right action of notation="LaTeX">$\mathop {\mathrm {GL}}\nolimi...