Quantum Independent Increment Processes on Superalgebras.
Quantum sections and Gauge algebras.
Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...
Rank two Ulrich modules over the affine cone of the simple node.
Regularity of the four dimensional Sklyanin algebra
Relative Buchsbaumness of bigraded modules
We study finitely generated bigraded Buchsbaum modules over a standard bigraded polynomial ring with respect to one of the irrelevant bigraded ideals. The regularity and the Hilbert function of graded components of local cohomology at the finiteness dimension level are considered.
Ringe mit verallgemeinerter Kupischreihe. II.
Rings Graded By a Generalized Group
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..
Seminormal graded rings and weakly normal projective varieties.
Smash products for -sets, Clifford theory and duality theorems.
Smash products, group actions and group graded rings.
Smooth invariants and -graded modules over
It is shown that every -graded module over is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian -groups.
Some algebraic applications of graded categorical group theory.
Some graded radicals of graded rings.
Some remarks on normal property of graded subalgebras of polynomial rings.
s-rings and modular representations.
Stable Clifford theory for divisorially graded rings.
Strongly graded left FTF rings.
An associated ring R with identity is said to be a left FTF ring when the class of the submodules of flat left R-modules is closed under injective hulls and direct products. We prove (Theorem 3.5) that a strongly graded ring R by a locally finite group G is FTF if and only if Re is left FTF, where e is a neutral element of G. This provides new examples of left FTF rings. Some consequences of this Theorem are given.
Strongly groupoid graded rings and cohomology
We interpret the collection of invertible bimodules as a groupoid and call it the Picard groupoid. We use this groupoid to generalize the classical construction of crossed products to what we call groupoid crossed products, and show that these coincide with the class of strongly groupoid graded rings. We then use groupoid crossed products to obtain a generalization from the group graded situation to the groupoid graded case of the bijection from a second cohomology group, defined by the grading...
Superlinear algebra or two-graded algebraic structures.
Sur certaines algèbres de Lie de dérivations
Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.