Related papers: Effect algebras with the maximality property

We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer $^*$-semigroups. We apply this general approach to study the full class of two-valued states and the…

Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not…

We give sufficient and necessary conditions to guarantee that a pseudo-effect algebra admits an $(n+1)$-valued discrete state. We introduce $n$-perfect pseudo-effect algebras as algebras which can be split into $n+1$ comparable slices. We…

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations $\ominus$ and $\oplus$ of L are uniquely determined by their system of neighbourhoods of 0 and form a…

In this article, we only consider finite effect algebras. We define the concepts of classical and quantum effect algebras and show that an effect algebra $E$ is classical if and only if there exists an observable that measures every effect…

We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

Quantum effects play an important role in quantum measurement theory. The set of all quantum effects can be organized into an algebraical structure called effect algebra. In this paper, we study various topologies on the Hilbert space…

Order unit spaces with comparability and spectrality properties as introduced by Foulis are studied. We define continuous functional calculus for order unit spaces with the comparability property and Borel functional calculus for spectral…

This paper defines the Euler-Poincar\'{e} characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions;…

We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's modularity result. In higher genus, we…

Given a finite poset $P$, its zeta matrix $\mathbf Z$ encode fundamental incidence-theoretic information about the order structure. In this paper we introduce and study the \emph{order-complement matrix} $\overline{\mathbf Z} = \mathbf J -…

We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space…

In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…

The paper studies projective freeness and Hermiteness of algebras of complex-valued continuous functions on topological spaces, Stein algebras, and commutative unital Banach algebras. New sufficient cohomology conditions on the maximal…

Zassenhaus conjectured that any unit of finite order in the integral group ring $\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra of $G$ to an element in $\pm G$. We review the known weaker versions of this…

We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…