A graded algebra with a non-rational Hilbert series

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

On a graded q-differential algebra

We construct the graded q-differential algebra on a ZN -graded algebra by means of a graded q-commutator. We apply this construction to a reduced quantum plane and study the first order differential calculus on a reduced quantum plane induced by the N -differential of the graded q-differential algebra. 1 Graded q-differential algebra In this section given a ZN -graded algebra we construct the g...

On the Lower Central Series Quotients of a Graded Associative Algebra

Let A be a noncommutative associative algebra, viewed as a Lie algebra via definition of the Lie bracket [x, y] = xy − yx. Define the lower central series filtration inductively by L1(A) = A, and Li+1(A) = [A,Li(A)]. Denote the components of its associated graded space by Bi(A) = Li(A)/Li+1(A). The components of the associated graded space are well understood in the cases when A = An = the free...

Hilbert Functions of Graded Algebras

Let R be a Noetherian commutative ring with identity, graded by the nonnegative integers N. Thus the additive group of R has a direct-sum decomposition R = R, + R, + ..., where RiRi C R,+j and 1 E R, . I f in addition R, is a field K, so that R is a k-algebra, we will say that R is a G-akebra. The assumption that R is Noetherian implies that a G-algebra is finitely generated (as an algebra over...

Differential Graded Algebra