Primary and strongly primary monoids domains play a central role in the ideal factorization theory of commutative domains. It is well-known that satisfying ascending chain condition on divisorial ideals (e.g., numerical monoids) are primary; multiplicative monoid non-zero elements one-dimensional local domain it if Noetherian. In present paper, we focus study additive submonoids non-negative ra...

This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under...

We consider a tower of generalized rook monoid algebras over the field $\mathbb{C}$ complex numbers and observe that Bratteli diagram associated to this is simple graph. construct modules describe Jucys-Murphy elements for algebras. Over an algebraically closed $\Bbbk$ positive characteristic $p$, utilizing algebras, $0\leq i\leq p-1$ we define corresponding $i$-restriction $i$-induction functo...

We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Γ is any graph not containing a four-cycle without chords, then the group G(Γ) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Γ) does not have a subgroup isomorphic to a direct product of non-abelian free groups. We also obtain corresponding...

Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. We begin by seeing weighted derivational algebras and weighted Rota–Baxter algebras as special monoids and special semigroups, respectively, for the same monoidal structure on the category of graph...

ΠMTL is a schematic extension of the monoidal t-norm based logic (MTL) by the characteristic axioms of product logic. In this paper we prove that ΠMTL satisfies the standard completeness theorem. From the algebraic point of view, we show that the class of ΠMTL-algebras (bounded commutative cancellative residuated l-monoids) in the real unit interval [0, 1] generates the variety of all ΠMTL-alge...

It is well known that clopen subgroups of finitely generated free profinite groups are again finitely generated free profinite groups. Clopen submonoids of free profinite monoids need not be finitely generated nor free. Margolis, Sapir and Weil proved that the closed submonoid generated by a finite code (which is in fact clopen) is a free profinite monoid generated by that code. In this note we...

For a given integer n = p1 1 p α2 2 . . . p αk k , (k ≥ 2), we give here a class of finitely presented finite monoids of order n. Indeed the monoids Mon(π), where π = 〈a1, a2, . . . , ak|a p αi i i = ai, (i = 1, 2, . . . , k), aiai+1 = ai, (i = 1, 2, . . . , k − 1)〉. As a result of this study we are able to classify a wide family of the kgenerated p-monoids (finite monoids of order a power of a...

Abstract Let G be a group and $$G_0 \subseteq G$$ G 0 ⊆ subset. A sequence over $$G_0$$ means finite of terms from , where the order elements is disregarded repetition allowed. product-one whose can ordered such that their product...