We prove that a trace monoid embeds into the queue monoid if and only if it embeds into the direct product of two free monoids. We also give a decidable characterization of these trace monoids.

This paper presents new results on the identities satisfied by sylvester and Baxter monoids. We show how to embed these monoids, of any rank strictly greater than 2, into a direct product copies corresponding monoid 2. confirms that all monoids same family, or equal satisfy exactly identities. then give complete characterization those identities, prove varieties generated have finite axiomatic ...

In this work, regularity of $n$-generalized Schützenberger product monoids from the point Group Theory is studied. Here, it determined necessary and sufficient conditions $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ to be regular while all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ are monoids. Also, by considering groups, given another result for product.

We discuss unique decomposition in partial commutative monoids. Inspired by a result from process theory, we propose the notion of decomposition order for partial commutative monoids, and prove that a partial commutative monoid has unique decomposition iff it can be endowed with a decomposition order. We apply our result to establish that the commutative monoid of weakly normed processes modulo...

The first step when forming the polynomial hierarchies of languages is to consider languages of the form KaL where K and L are over a finite alphabet A and from a given variety V of languages, a ∈ A being a letter. All such KaL’s generate the variety of languages BPol1(V ). We estimate the numerical parameters of the language KaL in terms of their values for K and L. These parameters include th...

The semi-direct product of arbitrary two monoids and a presentation for this product have received considerable attention, see for instance [12], [14] and [15]. In [15], Wang defined a trivialiser set of the Squier complex associated with this presentation. In this paper, as a main result, we discuss necessary and sufficient conditions for the standard presentation of the semi-direct product of...

For a monoid S, a (left) S-act is a non-empty set B together with a mapping S × B → B sending (s, b) to sb such that s(tb) = (st)b and 1b = b for all s, t ∈ S and b ∈ B. Right S-acts A can also be defined, and a tensor product A⊗S B (a set) can be defined that has the customary universal property with respect to balanced maps from A×B into arbitrary sets. Over the past three decades, an extensi...