Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ord...

Certain problems in connection with, for example, cooperating agents and distributed systems require reasoning about time which is measured on incomparable or unsynchronized time scales. In such situations, it is sometimes approporiate to use a temporal model that only provides a partial order on time points. We study the computational complexity of partially ordered temporal reasoning in expre...

We give a presentation of the endomorphism algebra EndUq(sl2)(V ), where V is the 3-dimensional irreducible module for quantum sl2 over the function field C(q 1 2 ). This will be as a quotient of the Birman-Wenzl-Murakami algebra BMWr(q) := BMWr(q , q2− q) by an ideal generated by a single idempotent Φq. Our presentation is in analogy with the case where V is replaced by the 2dimensional irredu...

The quantum double construction of a q-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The R-matrix thus obtained is compared with the existing literature. Recently there has been an increasing interest in the deformation of Lie (super)algebras[1, 2, 3, 4, 5, 6] and their quasitriangular Hopf algebra nature[7], mainly because of there wide applications in m...

A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential products are proved. We discuss sequentially ordered SEA’s in which the order is completely determined by the sequential product. It is demonstrated that int...

In the historical development of Riesz spaces, we can trace history ordered vector spaces to International Mathematical Congress in Bologna 1928. Studies related with f-Algebras for Dedekind complete space defined were initiated by Nakano and their current definition was made Amemiya, Birkhoff Pierce.The revival f-algebras, which had a tendency slow down period time, emerged as result Pagter's ...

When the parameter q ∈ C is not a root of unity, simple modules of affine q-Schur algebras have been classified in terms of Frenkel–Mukhin’s dominant Drinfeld polynomials ([6, 4.6.8]). We compute these Drinfeld polynomials associated with the simple modules of an affine q-Schur algebra which come from the simple modules of the corresponding q-Schur algebra via the evaluation maps.