scholarly journals Idempotent Generation in the Endomorphism Monoid of a Uniform Partition

2016 ◽  
Vol 44 (12) ◽  
pp. 5179-5198 ◽  
Author(s):  
Igor Dolinka ◽  
James East
Keyword(s):  
Endomorphism Monoid ◽  
Uniform Partition

The rank of the endomorphism monoid of a uniform partition

2008 ◽  
Vol 78 (3) ◽  
pp. 498-510 ◽  
Author(s):  
João Araújo ◽  
Csaba Schneider
Keyword(s):  
Endomorphism Monoid ◽  
Uniform Partition

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.

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
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