A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number [Formula: see text], the additive text] of evaluation semiring atomic. The structure both and multiplicative monoids has been subject several recent papers. Here we focus study its omega-primality elasticity, aiming to better underst...

We introduce the notion of an orthogonal completion of an inverse monoid with zero. We show that the orthogonal completion of the polycyclic monoid on n generators is isomorphic to the inverse monoid of right ideal isomorphisms between the finitely generated right ideals of the free monoid on n generators, and so we can make a direct connection with the Thompson groups Vn,1. 2000 AMS Subject Cl...

Abstract Let H be a cancellative commutative monoid, let $$\mathcal {A}(H)$$ A ( H ) the set of atoms and $$\widetilde{H}$$ ~ root closure . Then is called transfer Krull if there exists homomor...

Throughout this paper, the ring R is not necessarily with an identity. We denote the set of all idempotents of R by E(R). Also, for a subset X ⊆ R, we denote the right (resp., left) annihilator of X in R by annr(X) (resp., ann (X)). Now, according to Fraser and Nicholson in [5], we call a ring R a left p.p.-ring, in brevity, l.p.p.-ring, if for all x ∈ R, there exists an idempotent e such that ...

It is shown that all nontrivial elements in higher K-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties. 1. Statement of the main result The nilpotence conjecture in K-theory of toric varieties, treated in our previous works, asser...

The main result of this paper gives a presentation for an arbitrary subgroup of a monoid defined by a presentation. It is a modification of the well known Reidemeister–Schreier theorem for groups. Some consequences of this result are explored. It is proved that a regular monoid with finitely many left and right ideals is finitely presented if and only if all its maximal subgroups are finitely p...

Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents wh...

We develop a counterpart to Garside’s analysis of the braid monoid B n relevant for the monoid MLD that describes the geometry of the left self-distributivity identity. The monoid MLD extends B ∞, of which it shares many properties, with the exception that it is not a direct limit of finitely generated monoids. By introducing a convenient local version of the fundamental elements ∆, we prove th...