Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

Given M copies of a q-deformed Weyl or Clifford algebra in the defining representation of a quantum group Gq, we determine a prescription to embed them into a unique, inclusive Gq-covariant algebra. The different copies are “coupled” to each other and are naturally ordered into a “chain”. In the case Gq = SLq(N) a modified prescription yields an inclusive algebra which is even explicitly SLq(M)...

A diagonal representation of the quantum mechanical density matrix by means of standard bosonic oscillator coherent states was obtained by Sudarshan [1] and Glauber [2]. A remarkable feature of this representation is that the average expectation value of normal ordered operators becomes the same as that of a classical function for a probability distribution over complex plane, thereby bringing ...

Consider the coradical filtration of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We show that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980’s by Grossman and Larson. These Hopf algebras are constructed from ordered trees and heap-ordered trees, respectively. We also sho...

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...

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...