Given a finitely presented monoid and a homotopy base for the monoid, and given an arbitrary Schützenberger group of the monoid, the main result of this paper gives a homotopy base, and presentation, for the Schützenberger group. In the case that the R-class R of the Schützenberger group G (H) has only finitely many H -classes, and there is an element s of the multiplicative right pointwise sta...

A pomonoid S is a monoid equipped with a partial order that is compatible with the binary operation. In the same way that M -acts over a monoid M correspond to the representation of M by transformations of sets, S-posets correspond to the representation of a pomonoid S by order preserving transformations of posets. Following standard terminology from the theories of R-modules over a unital ring...

In this paper we construct, for any 1 m; n 1, a nitely presented monoid with left cohomological dimension m and right cohomological dimension n.

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

For a tournament T , let ν3(T ) denote the maximum number of pairwise arc-disjoint triangles in T . Let ν3(n) denote the minimum of ν3(T ) ranging over all regular tournaments with n vertices (n odd). It is conjectured that ν3(n) = (1 + on(1))n /9 and proved that n 11.43 (1− on(1)) ≤ ν3(n) ≤ n 9 (1 + on(1)) improving upon the best known upper bound and lower bound. The result is generalized to ...

In this paper we show that ωBand ωS-regular languages satisfy the following separation-type theorem If L1, L2 are disjoint languages of ω-words both recognised by ωB(resp. ωS)automata then there exists an ω-regular language Lsep that contains L1, and whose complement contains L2. In particular, if a language and its complement are recognised by ωB(resp. ωS)automata then the language is ω-regula...

In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.

In this paper we have introduced fuzzy quasi-ideal and fuzzy left(right, two-sided) ideals in LA-semigroup. We have proved some results related to fuzzy quasi-ideals and fuzzy left(right, two-sided) ideals of an LA-semigroup. Further we characterize an intra-regular LA-semigroup by the properties of their fuzzy ideals.

Many important families of regular languages have effective characterizations in terms of syntactic monoids or syntactic semigroups (see e.g. [1]). Definition of the syntactic monoid (resp. syntactic semigroup) of a language L ⊆ X * (resp. a language L ⊆ X +) over an alphabet X requires regarding L as a subset of the free monoid X * (resp. free semigroup X +). On the other hand tree languages h...