The authors use techniques and results from the theory of generalized metric spaces to give a new, short proof that every connected, linearly ordered topological space that is a cancellative topological semigroup is metrizable, and hence embeddable in R. They also prove that every separable, linearly ordered topological space that is a cancellative topological semigroup is metrizable, so embedd...

Profinite semigroups provide powerful tools to understand properties of classes of regular languages. Until very recently however, little was known on the structure of “large” relatively free profinite semigroups. In this paper, we present new results obtained for the class of all finite aperiodic (that is, group-free) semigroups. Given a finite alphabet X, we focus on the following problems: (...

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

Suppose A 1 ; ; A s are (1;?1) matrices of order m satisfying (4) Call A 1 ; ;A s a regular s-set of matrices of order m if (1), (2), (3) are satissed and a regular s-set of regular matrices if (4) is also satissed, these matrices were rst discovered by J. Seberry and A. L. Whiteman in \New Hadamard matrices and conference matrices obtained via Mathon's construction", Graphs and Combinatorics, ...

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating cong...