All Countable Monoids Embed in the Monoid of the Infinite Random Graph
نویسندگان
چکیده
We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.
منابع مشابه
All countable monoids embed into the monoid of the infinite random graph
We prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of End(R), the endomorphism monoid of the infinite random graph R. Consequently, End(R) embeds each countable monoid, satisfies no nontrivial monoid identity, and has an undecidable universal theory.
متن کاملOn zero divisor graph of unique product monoid rings over Noetherian reversible ring
Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...
متن کاملA note on orientations of the infinite random graph
We answer a question of P. Cameron’s by giving examples of 2א0 many non-isomorphic acyclic orientations of the infinite random graph with a topological ordering that do not have the pigeonhole property. Our examples also embed each countable linear ordering. A graph is n-existentially closed or n-e.c. if for each n-subset S of vertices, and each subset T of S (possibly empty), there is a vertex...
متن کاملOn Graphs With a Given
On Graphs With A Given Endomorphism Monoid Benjamin Shemmer Hedrĺın and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. We will give a construction G(M) for a graph with prescribed endomorphism monoid M. Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism mo...
متن کاملThe n-ordered graphs: A new graph class
For a positive integer n, we introduce the new graph class of n-ordered graphs, which generalize partial n-trees. Several characterizations are given for the finite n-ordered graphs, including one via a combinatorial game. We introduce new countably infinite graphs R, which we name the infinite random n-ordered graphs. The graphs R play a crucial role in the theory of n-ordered graphs, and are ...
متن کامل