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Generalized deductive systems in subregular varieties

Ivan Chajda (2003)

Mathematica Bohemica

An algebra 𝒜 = ( A , F ) is subregular alias regular with respect to a unary term function g if for each Θ , Φ ∈ Con 𝒜 we have Θ = Φ whenever [ g ( a ) ] Θ = [ g ( a ) ] Φ for each a ∈ A . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset C ⊆ A is a class of some congruence on Θ containing g ( a ) if and only if C is this generalized deductive system. This method is efficient (needs a finite number of steps).

Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra E n d R A of the R-module R A , taking any a ∈ A to the right multiplication a r ∈ E n d R A by a, is an isomorphism of algebras. In this case R A is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...

Generalized homogeneous, prelattice and MV-effect algebras

Zdena Riečanová, Ivica Marinová (2005)

Kybernetika

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra P is a union of generalized MV-effect algebras and...

Generalized projections of Borel and analytic sets

Marek Balcerzak (1996)

Colloquium Mathematicae

For a σ-ideal I of sets in a Polish space X and for A ⊆ X 2 , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where A x =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a ∑ 2 0 -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ ∑ 1 1 ( X 2 ) ] = ∑ 1 1 ( X ) for a wide class of ∑ 2 0 -supported σ-ideals.

Generalized version of the compatibility theorem. Two examples.

Carlo Bertoluzza, Antonella Bodini (1996)

Mathware and Soft Computing

In a previous work ([3]) we proved that the Nguyen's condition for [f(tilde-A)]α to be equal to f(Aα) also holds for the most general class of the L-fuzzy subsets, where L is an arbitrary lattice. Here we recall the main points of the proof ad present some examples ralated to non-linear lattices.

Generated fuzzy implications and fuzzy preference structures

Vladislav Biba, Dana Hliněná (2012)

Kybernetika

The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet ( p , i , j ) , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.

Generated triangular norms

Erich Peter Klement, Radko Mesiar, Endre Pap (2000)

Kybernetika

An overview of generated triangular norms and their applications is presented. Several properties of generated t -norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.

Generating countable sets of surjective functions

J. D. Mitchell, Y. Péresse (2011)

Fundamenta Mathematicae

We prove that any countable set of surjective functions on an infinite set of cardinality ℵₙ with n ∈ ℕ can be generated by at most n²/2 + 9n/2 + 7 surjective functions of the same set; and there exist n²/2 + 9n/2 + 7 surjective functions that cannot be generated by any smaller number of surjections. We also present several analogous results for other classical infinite transformation semigroups such as the injective functions, the Baer-Levi semigroups, and the Schützenberger monoids.

Currently displaying 21 – 40 of 83