A set E equipped with a partial, commutative and associative operation ⊕, containing elements 0 and 1, in which the existence of a unique inverse element x′ to any x ∈ E is guaranteed, and a⊕ 1 is admitted only if a = 0 is well known as effect algebra. Effect algebras were introduced by Foulis and Bennet [3] and simultaneously by Kôpka and Chovanec [7] as D-posets. An effect algebra equipped wi...

We prove some Schur positivity results for the chromatic symmetric function X G of a (hyper)graph G, using connections to group algebra group. The first such connection works (hyper)forests F: we describe coefficients F in terms eigenvalues product Hermitian idempotents algebra, one factor each edge (a more general formula similar shape holds all chordal graphs). Our main application this techn...

The framework. In 1956, G. Birkhoff G. and R.S. Pierce [1] conjectured the following: do the algebra of piecewise polynomial functions with real coefficients and the algebra of functions that can be written as Inf and Sup of finitely many polynomials coincide? The conjecture – that can be equivalently stated asking for the free n-generated lattice-ordered algebra to be isomorphic with the algeb...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characte...

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra. The main results are the classification of the irreducible modules, a version of Steinberg’s Tensor Product Theorem, and the construction of positive characte...

MV-algebras were introduced by Chang in 1958 preliminary to his providing an algebraic completeness proof for the K0-vaΓued Lukasiewicz propositional logic, LXo. In this paper a method is given for determining, for an arbitrary normal extension of LKo, an MV-algebra characteristic for the extension. The characteristic algebras are finite direct products of two sets of linearly ordered MV-algebr...

In this study, we define the generalized symmetric bi-derivation and its trace on MV-algebras give examples. We investigate some properties of bi-derivation’s trace. introduce isotone bi-additive bi-derivation. show that if A is a linearly ordered MV-algebra, Γ related to D γ , then = 0 or γ1 1

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Georgescu and Iorgulescu [3] introduced pseudo-BCK-algebras (in a slightly different way) as a non-commutative generalization of BCK-algebras, in the sense that if →= , then the algebra (A,→, 1) is a BCK-algebra. Pseudo-BCK-algebras relate to (non-commutative) residuated lattices as BCK-algebras do to commutative residuated lattices; specifically, by [6], pseudoBCK-algebras are just the 〈→, , 1...

We study observables as r-D-homomorphisms de®ned on Boolean D-posets of subsets into a Boolean Dposet. We show that given an atomic r-complete Boolean D-poset P with the countable set of atoms there exist a r-complete Boolean D-poset of subsets S and a r-D-homomorphism h from S onto P, more precisely we can choose S ˆ B…R†, which gives an analogy of the Loomis± Sikorski representation theorem f...