We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is a transitive forest. As a consequence we obtain the first example of a finitely presented group with a decidable generalized word problem that does not have ...

Uncertainty associated with fuzzy membership functions for a water quality management problem is addressed through interval grey numbers. The lower and upper bounds of the membership functions are expressed as interval grey numbers, and the membership functions are modeled as imprecise membership functions. A grey fuzzy optimization model for water quality management of a river system is develo...

In distributed systems, a group of computer should continue to do cooperation in order to finish some jobs. In such a system, a group membership protocol is especially practical and important elements to provide processes in a group with a consistent common knowledge about the membership of the group. Whenever a membership change occurs, processes should agree on which of them should do to acco...

This paper introduces the concept of subalgebra and discusses some properties subalgebra. We also examine different types ideals how they behave. describe a homomorphism. Finally, we present quotient algebra discuss isomorphism theorems.

The main problem, deforming a subalgebra of a Lie algebra, is treated algebraically, requiring an extensive ” development of methods of defining multiplications on Lie algebra cohomolo,gy cochains. Some applications to differential geometry are also presented. To be submitted to Communications in Math. Physics. * Work supported by the U. S. Atomic Energy Commission.

W e present a deterministic polynomial-time algorithm for the ABC problem, which is the membership problem for 2-generated commutative linear semigroups over an algebraic number field. W e also obtain a polynomial t ime algorithm for the (easier) membership problem for 2-generated abelian linear groups. Furthermore, we provide a polynomial-sized encoding for the set of all solutions.

We present an algebraic approach to string theory, using a Hamiltonian reduction of N = 2 WZW models. An embedding of sl(1|2) in a Lie superalgebra determines a niltopent subalgebra. Chirally gauging this subalgebra in the corresponding WZW action leads to an extension of the N = 2 superconformal algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this provides an exhaust...

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’1-CA0 over RCA0.

B. Jónsson has asked : Is there an algebra of power a with no proper subalgebra of power a? H. J. Keisler and F. Rowbottom proved that the answer is affirmative for every a, provided Gödel's constructibility axiom holds [1]. The main aim of this paper is to prove, using the generalized continuum hypothesis (G .C .H. in what follows), that the answer is affirmative for each non limit cardinal (s...

We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.