The endomorphism monoid of a free trioid of rank 1

2016 ◽  
Vol 76 (3) ◽  
pp. 355-366 ◽  
Author(s):  
Yurii V. Zhuchok
Keyword(s):  
Endomorphism Monoid

scholarly journals Products of two idempotent transformations over arbitrary sets and vector spaces

1998 ◽  
Vol 57 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Rachel Thomas
Keyword(s):  
Vector Space ◽  
Transformation Semigroup ◽  
Vector Spaces ◽  
Endomorphism Monoid ◽  
Linear Transformations ◽  
Arbitrary Vector ◽  
Full Transformation ◽  
Full Transformation Semigroup

In this paper we consider the characterisation of those elements of a transformation semigroup S which are a product of two proper idempotents. We give a characterisation where S is the endomorphism monoid of a strong independence algebra A, and apply this to the cases where A is an arbitrary set and where A is an arbitrary vector space. The results emphasise the analogy between the idempotent generated subsemigroups of the full transformation semigroup of a set and of the semigroup of linear transformations from a vector space to itself.

scholarly journals A note on subgroups of automorphism groups of full shifts

2016 ◽  
Vol 38 (4) ◽  
pp. 1588-1600 ◽  
Author(s):  
VILLE SALO
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Endomorphism Monoid ◽  
Direct Products ◽  
Free Products ◽  
Group Case ◽  
Sofic Shift ◽  
Full Shift

We discuss the set of subgroups of the automorphism group of a full shift and submonoids of its endomorphism monoid. We prove closure under direct products in the monoid case and free products in the group case. We also show that the automorphism group of a full shift embeds in that of an uncountable sofic shift. Some undecidability results are obtained as corollaries.

Absolute graphs with prescribed endomorphism monoid

2007 ◽  
Vol 76 (2) ◽  
pp. 256-267 ◽  
Author(s):  
Manfred Droste ◽  
Rüdiger Göbel ◽  
Sebastian Pokutta
Keyword(s):  
Endomorphism Monoid

Idempotent rank in endomorphism monoids of finite independence algebras

2007 ◽  
Vol 137 (2) ◽  
pp. 303-331 ◽  
Author(s):  
R. Gray
Keyword(s):  
Proper Ideal ◽  
Endomorphism Monoid ◽  
Endomorphism Monoids ◽  
Idempotent Rank

In 1992, Fountain and Lewin showed that any proper ideal of an endomorphism monoid of a finite independence algebra is generated by idempotents. Here the ranks and idempotent ranks of these ideals are determined. In particular, it is shown that when the algebra has dimension greater than or equal to three the idempotent rank equals the rank.

scholarly journals IDEMPOTENT RANK IN THE ENDOMORPHISM MONOID OF A NONUNIFORM PARTITION

2015 ◽  
Vol 93 (1) ◽  
pp. 73-91 ◽  
Author(s):  
IGOR DOLINKA ◽  
JAMES EAST ◽  
JAMES D. MITCHELL
Keyword(s):  
Endomorphism Monoid ◽  
Generating Sets ◽  
Idempotent Rank ◽  
Finite Set ◽  
Uniform Case

We calculate the rank and idempotent rank of the semigroup ${\mathcal{E}}(X,{\mathcal{P}})$ generated by the idempotents of the semigroup ${\mathcal{T}}(X,{\mathcal{P}})$ which consists of all transformations of the finite set $X$ preserving a nonuniform partition ${\mathcal{P}}$. We also classify and enumerate the idempotent generating sets of minimal possible size. This extends results of the first two authors in the uniform case.

scholarly journals On the number of graphs with a given endomorphism monoid

2010 ◽  
Vol 310 (3) ◽  
pp. 376-384
Author(s):  
Václav Koubek ◽  
Vojtěch Rödl
Keyword(s):  
Endomorphism Monoid

scholarly journals v*-ALGEBRAS, INDEPENDENCE ALGEBRAS AND LOGIC

2011 ◽  
Vol 21 (07) ◽  
pp. 1237-1257 ◽  
Author(s):  
JOÃO ARAÚJO ◽  
MÁRIO EDMUNDO ◽  
STEVEN GIVANT
Keyword(s):  
Vector Space ◽  
Universal Algebra ◽  
Semigroup Theory ◽  
Endomorphism Monoid ◽  
Transformation Monoid ◽  
Middle Period ◽  
The 1960S

Independence algebras were introduced in the early 1990s by specialists in semigroup theory, as a tool to explain similarities between the transformation monoid on a set and the endomorphism monoid of a vector space. It turned out that these algebras had already been defined and studied in the 1960s, under the name of v*-algebras, by specialists in universal algebra (and statistics). Our goal is to complete this picture by discussing how, during the middle period, independence algebras began to play a very important role in logic.

scholarly journals End-regular and End-orthodox generalized lexicographic products of bipartite graphs

2016 ◽  
Vol 14 (1) ◽  
pp. 229-236 ◽  
Author(s):  
Rui Gu ◽  
Hailong Hou
Keyword(s):  
Orthodox Semigroup ◽  
Bipartite Graphs ◽  
Endomorphism Monoid

AbstractA graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.

REPRESENTING SUBDIRECT PRODUCT MONOIDS BY GRAPHS

2009 ◽  
Vol 19 (05) ◽  
pp. 705-721 ◽  
Author(s):  
VÁCLAV KOUBEK ◽  
VOJTĚCH RÖDL ◽  
BENJAMIN SHEMMER
Keyword(s):  
Subdirect Product ◽  
Abelian Groups ◽  
Endomorphism Monoid ◽  
Completely Simple Semigroups ◽  
Finite Monoids ◽  
Minimum Number ◽  
Completely Simple

Hedrlín and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. In a previous paper, we give a construction G(M) for a graph with prescribed endomorphism monoid M known as a [Formula: see text]-graph. Using this construction, we derived bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. In this paper, we generalize the [Formula: see text]-graph construction and derive several new bounds for monoid classes not handled by our first paper. Among these are the so called "strong semilattices of C-semigroups" where C is one of the following: Groups, Abelian Groups, Rectangular Groups, and completely simple semigroups.

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