Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Boolean algebras

Sortuj według:

Ogranicz wyniki do:

Distributivity versus associativity in the homology theory of algebraic structures

Przytycki J. H.

Demonstratio Mathematica

2011

Vol. 44, nr 4

824-869

While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson. We develop this theory in the historical context and propose a general framework to study homology of distributive structures. We illustrate the theory by computing some examples of 1-term and 2-term homology, and then discussing 4-term homology for Boolean algebras. We outline potential relations to Khovanov homology, via the Yang-Baxter operator.

On the compactness and countable compactness of 2R in ZF

Keremedis K., Felouzis E., Tachtsis E.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 4

293-302

In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements "2R is countably compact" and "2R is compact".

Algebraic proofs of Kwapień's and Lamperti's representations theorems

Mehemmed A.

Demonstratio Mathematica

1999

Vol. 32, nr 2

401-412

The main purpose of this paper is to give proofs of modification of Kwapień's representation theorem for continuous linear operators on Lo , and modification of the Lamperti representation theorem for linear operators between Lp spaces.The previous proofs of these theorems were given, using the methods of functional analysis. In our paper we would like to show that they can be proved also by algebraic methods, with an aid of the theory of Boolean algebras and measure theory. In the proofs we use a theorem from [7].

The lifting problem with the full ideal

Shelah S.

Journal of Applied Analysis

1998

Vol. 4, nr 1

1-17

We show that there are a cardinal μ, a σ-ideal I ⊆ P(μ) and a σ-subalgebra B of subsets of μ extending I such that B/I satisfies the c.c.c. but the quotient algebra B/I has no lifting.