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...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...

For G a locally compact group and G its dual, let Jd(G) be the C*algebra generated by the Fourier-Stieltjes transforms of the discrete measures on G. We show that the canonical trace on ,4(G) is faithful if and only if G is amenable as a discrete group. We further show that if G is nondiscrete and amenable as a discrete group, then the only measures in dKd(G) are the discrete measures, and also...

An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...

This paper deals with Zadeh’s compositional rule of inference [12] under triangular norms: IF X is P AND X and Y have relation R, THEN Y is Q, where P and Q are fuzzy sets of the real line IR, R is a fuzzy relation on IR and the conclusion Q is defined via sup-T composition of P and R: μQ(y) = sup x∈IR T (μP (x), μR(x, y)), y ∈ IR. It is shown that (i) when the triangular norm T and the members...

In Section 2 replace the definition of ∗◦Q in Definition 1 by x∗◦Q y = inf{u ∗◦ v | u > x, v > y}. It is defined only if the infimum exists. Proposition 1 remains unchanged. Theorem 0. Let (X, ∗◦,→∗◦,≤) be a commutative residuated semigroup on a complete chain equipped with the order topology. Let a, b, c ∈ X be such that a = b→∗◦ c. Let (x, y) ∈ X × X be such that 1. neither x nor y equals the...