In analogy with effect algebras, we introduce the test spaces and $MV$-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between $MV$-algebras and $MV$-test spaces.
Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is {\it uniformly Archimedean} then it is sharply dominating.
A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra with a finite number of operations into an algebra of the same type can be described.
A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 \subset L1 \subset...\subset Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H + Li-1 or H ∩ Li = H ∩ Li-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable., Sara Chehrazi, Ali Reza Salemkar., and Obsahuje seznam literatury
Let Ln = K[x1±1,..., xn±1] be a Laurent polynomial algebra over a field K of characteristic zero, Wn:= DerK(Ln) the Lie algebra of K-derivations of the algebra Ln, the so-called Witt Lie algebra, and let Vir be the Virasoro Lie algebra which is a 1-dimensional central extension of the Witt Lie algebra. The Lie algebras Wn and Vir are infinite dimen- sional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: AutLie(Vir) \simeq AutLie(W1) \simeq {±1} \simeq K*, and give a short proof that AutLie(Wn) \simeq AutK-alg(Ln) \simeq GLn(Z) \ltimes K*n., Vladimir V. Bavula., and Obsahuje seznam literatury
We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index., Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz., and Obsahuje seznam literatury
According to formalism a mathematician is not concerned with mysterious meta-physical entities but with mathematical symbols themselves. Mathematical entities, on this view, become mere sensible signs. However, the price that has to be paid for this move looks to be too high. Mathematics, which is nowadays considered to be the queen of the sciences, thus turns out to be a content-less game. That is why it seems too absurd to regard numbers and all mathematical entities as mere symbols. T e aim of our paper is to show the reasons that have led some philosophers and mathemati¬cians to accept the view that mathematical terms in a proper sense do not refer to anything and mathematical propositions do not have any real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science.