Graph products of monoids
WebMar 14, 2008 · Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull … WebGraph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups then any graph product is a group. For monoids that are not groups, regularity is perhaps the first and most important algebraic property that one considers: …
Graph products of monoids
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WebOct 9, 2009 · Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that … WebDec 14, 2024 · In the special case where all the individual monoids of our graph of monoids are positive cones of subgroups of $({\mathbb {R}},+)$ , we obtain, under some extra assumptions, the following stronger results. We determine all closed invariant subspaces of the unit space of the groupoid attached to our graph of monoids …
WebMar 20, 2013 · In this paper, we mainly investigate the interplay between the semi-direct product over monoids and the graph-theoretic properties of the semi-direct product in terms of its relations. ... Wang J: Finite derivation type for semi-direct products of monoids. Theor. Comput. Sci. 1998, 191(1–2):219–228. 10.1016/S0304-3975(97)00164-3. Weba semigroup presentation. The construction of graph products of semigroups is funda-mentally di erent to that of graph products of monoids, since semigroups are an algebra with a di erent signature to that of monoids. We will see in Remark 2.4 that each vertex semigroup embeds into the graph product. A graph product of monoids or, indeed, of
WebAug 15, 2002 · On graph products of automatic monoids - Volume 35 Issue 5. We use cookies to distinguish you from other users and to provide you with a better experience on our websites. http://export.arxiv.org/abs/2102.06409v3
Webin graph products of monoids have a left Foata normal; previously this was an important tool in the study of graph monoids, and the same holds here. The structure of this paper is as follows.
WebMay 23, 2006 · Abstract. It is shown that the graph product of automatic monoids is always automatic thereby improving on a result by Veloso da Costa [22] who showed this result provided the factors have finite geometric type. Secondly, we prove that, in general, the free product (and therefore the graph product) of biautomatic monoids need not be … dick\u0027s sporting goods vestsWebDefinition. Given a finite simplicial graph G with a group (or monoid) attached to each vertex, the associated graph product is the group (monoid) gen-erated by each of the vertex groups (monoids) with the added relations that elements of distinct adjacent vertex groups commute. Graph products were defined by Green [15], and have also been ... city car taxiWebFeb 12, 2024 · Graph products of monoids provide a common framework for direct and free products, and graph monoids (also known as free partially commutative monoids). If the monoids in question are groups, then ... dick\u0027s sporting goods venice flWebSep 15, 2024 · A partial automorphism of a finite graph is an isomorphism between its vertex-induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the algebraic structure of such inverse monoids by the means of standard tools of inverse semigroup theory, … city cars wienWebGraph theory 8.1. Circuits in undirected graphs ... Dependent products of monoids; 9.34. Dependent products of semigroups; 9.35. The dihedral group construction; 9.36. The dihedral groups; 9.37. The E₈-lattice; 9.38. Embeddings of abelian groups; 9.39. Embeddings of groups; 9.40. The endomorphism rings of abelian groups; citycar telefoneWebproducts of monoids (Section 2.3). The graph product construction is a well-known construction in mathematics, see e.g. [26,28], that generalizes both free products and direct products: An independence relation on the factors of the graph product specifies, which monoids are allowed to commute elementwise. Section 3 deals with existential ... city cars wloclawek opinieWebhow the monoids of composed graphs (e.g. product graphs) relate to algebraic com-positions (e.g. products) of the monoids of the components. This type of question can be interpreted as follows: when is the formation of the monoid product-preserving? In Chapter 11 we come back to the formation of Cayley graphs of a group or semi-group. city cartage company mt sterling ky