A nonerasing morphism σ is said to be weakly unambiguous with respect to a word s if σ is the only nonerasing morphism that can map s to σ(s), i. e., there does not exist any other nonerasing morphism τ satisfying τ(s) = σ(s). In the present paper, we wish to characterise those words with respect to which there exists such a morphism. This question is nontrivial if we consider so-called length-...

@0-categorical o-minimal structures were completely described in 4], and are essentially built up from copies of the rationals as an ordered set by`cutting and copying'. Here we investigate the possible structures which an @0-categorical weakly o-minimal set may carry, and nd that there are some rather more interesting (and not o-minimal) examples. We show that even here the possibilities are l...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

We present a proof of certain congruences modulo powers of an odd prime for the coefficients of a series produced by repeated application of U -operator to a certain weakly holomorphic modular form. This kind of congruences were first observed by Kaneko as a result of numerical experiments, and later proved in a different (but similar) case by Guerzhoy [6]. It is interesting to note that, in ou...

We associate to every equicharacteristic zero Noetherian local ring R a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a weakly functorial way. Since such ultraproducts carry naturally a non-standard Frobenius, we can define a new tight closure operation on R by mimicking the positive characteristic functional definition of tight closure. T...

In this paper we complete the characterization of Ext(G, Z) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals (νp : p ∈ Π) satisfying νp ≤ 2 , ...

We show that an ideal I of an MV -algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I = {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combin...

In this paper, the study of vague structures of Γ-semigroups is initiated by introducing the concepts of vague subsemigroup, vague bi-ideal and vague (1, 2)-ideal in a Γ-semigroup and some fundamental results are obtained. Then the concept of vague weakly completely prime ideals in Γ-semigroups has been introduced and studied directly and via operator semigroups

We give a construction of 3-class and 4-class association schemes from s-nonlinear and differentially 2s-uniform functions, and a construction of p-class association schemes from weakly regular p-ary bent functions, where p is an odd prime.

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...