Displaying similar documents to “Free systems of algebras and ultraclosed classes.”

Finiteness of the strong global dimension of radical square zero algebras

Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia (2004)

Open Mathematics

Similarity:

The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem...

Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

Similarity:

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not...

Dual commutative hyper K-ideals of type 1 in hyper K-algebras of order 3.

L. Torkzadeh, M. M. Zahedi (2006)

Mathware and Soft Computing

Similarity:

In this note we classify the bounded hyper K-algebras of order 3, which have D = {1}, D = {1,2} and D = {0,1} as a dual commutative hyper K-ideal of type 1. In this regard we show that there are such non-isomorphic bounded hyper K-algebras.

Tensor product construction of 2-freeness

R. Lenczewski (1998)

Banach Center Publications

Similarity:

From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.

BCI-homomorphisms

Yuzhong Ding, Fuguo Ge, Chenglong Wu (2008)

Formalized Mathematics

Similarity:

In this article the notion of the power of an element of BCI-algebra and its period in the book [11], sections 1.4 to 1.5 are firstly given. Then the definition of BCI-homomorphism is defined and the fundamental theorem of homomorphism, the first isomorphism theorem and the second isomorphism theorem are proved following the book [9], section 1.6.MML identifier: BCIALG 6, version: 7.9.03 4.108.1028

Tail and free poset algebras.

Mohamed Bekkali, Driss Zhani (2004)

Revista Matemática Complutense

Similarity:

We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semi-lattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T).