In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...

Some Realization of gl q (n)-covariant Oscillator Algebra and gl q (n)-covariant q-Virasoro Algebra with q a root of unity. Abstract In this paper some realization of gl q (n)-covariant oscillators is obtained when q is a root of unity. And the gl q (n)-covariant q-Virasoro algebra is presented by using the gl q (n)-covariant oscillators.

In a paper entitled Noncommutative valuations, Schilling [8] proved that if an algebra of finite order over its center is relatively complete in a valuation (where the value group of the nonarchimedean, exponential valuation is not assumed to be commutative) then the value group is commutative. A similar type of theorem, proved by Albert [l], states that if an algebra of finite order over a fie...

A Leonard pair is an ordered of diagonalizable linear maps on a finite-dimensional vector space, that each act eigenbasis for the other one in irreducible tridiagonal fashion. In present paper we consider type pair, said to have spin. The notion spin model was introduced by V.F.R. Jones construct link invariants. symmetric matrix over C satisfies two conditions, called II and III conditions. It...

We study a q-analog Qr(n, q) of the partition algebra Pr(n). The algebra Qr(n, q) arises as the centralizer algebra of the finite general linear group GLn(Fq) acting on a vector space IR q coming from r-iterations of Harish-Chandra restriction and induction. For n ≥ 2r, we show that Qr(n, q) has the same semisimple matrix structure as Pr(n). We compute the dimension dn,r(q) = dim(IR r q ) to be...

where β = q+q and δ = −(q − q) 2 . (TD) can be regarded as a q-analogue of the DolanGrady relations and we call A the q-Onsager algebra. We classify the finite-dimensional irreducible representations of A. All such representations are explicitly constructed via embeddings of A into the Uq(sl2)-loop algebra. As an application, tridiagonal pairs of qRacah type over C are classified in the case wh...

Interval arithmetic is based on the fact that for intervals on the real line, the element-wise product of two intervals is also an interval. This property is not always true: e.g., it is not true if we consider intervals on the set of integers instead of intervals on the set of real numbers. When is an element-wise product or a sum of two intervals always an interval? In this paper, we analyze ...

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 a class of endomomorphism algebras of certain q-permutation modules over the Hecke algebra of type B, whose summands involve both parabolic and quasi-parabolic subgroups, and prove that these algebras are integrally free and quasi-hereditary, and are stable under base change. Some consequences for decomposition numbers are discussed. The notion of a q-Schur algebra was introduced by Di...

We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), w...