Free rectangular doppelsemigroups

2019 ◽  
Vol 19 (11) ◽  
pp. 2050205 ◽  
Author(s):  
Anatolii V. Zhuchok ◽  
Yuliia V. Zhuchok ◽  
Jörg Koppitz
Keyword(s):  
Endomorphism Semigroup

A doppelsemigroup is a nonempty set equipped with two binary associative operations satisfying certain identities. In this paper, we consider the variety of rectangular doppelsemigroups which are analogs of rectangular semigroups. We construct the free rectangular doppelsemigroup and characterize the least rectangular congruence on the free doppelsemigroup. As a consequence, the free rectangular semigroup is presented. We also describe all (maximal) subdoppelsemigroups, all idempotents and all endomorphisms of the free rectangular doppelsemigroup, and give a criterion for an isomorphism of endomorphism semigroups of free rectangular doppelsemigroups. In addition, we show that the endomorphism semigroup of the free rectangular doppelsemigroup is not regular in general.

scholarly journals A note on generators of the endomorphism semigroup of an infinite countable chain

2017 ◽  
Vol 16 (02) ◽  
pp. 1750031
Author(s):  
Ilinka Dimitrova ◽  
Vítor H. Fernandes ◽  
Jörg Koppitz
Keyword(s):  
Infinite Chain ◽  
Sufficient Condition ◽  
Endomorphism Semigroup ◽  
Necessary And Sufficient Condition ◽  
Countable Chain ◽  
Necessary And Sufficient

In this note, we consider the semigroup [Formula: see text] of all order endomorphisms of an infinite chain [Formula: see text] and the subset [Formula: see text] of [Formula: see text] of all transformations [Formula: see text] such that [Formula: see text]. For an infinite countable chain [Formula: see text], we give a necessary and sufficient condition on [Formula: see text] for [Formula: see text] to hold. We also present a sufficient condition on [Formula: see text] for [Formula: see text] to hold, for an arbitrary infinite chain [Formula: see text].

On the endomorphism semigroup of simple algebras

1967 ◽  
Vol 170 (4) ◽  
pp. 334-338 ◽  
Author(s):  
George Gr�tzer
Keyword(s):  
Endomorphism Semigroup ◽  
Simple Algebras

ON AUTOMORPHISMS OF THE ENDOMORPHISM SEMIGROUP OF A FREE UNIVERSAL ALGEBRA

2007 ◽  
Vol 17 (05n06) ◽  
pp. 1085-1106 ◽  
Author(s):  
G. MASHEVITZKY ◽  
B. I. PLOTKIN
Keyword(s):  
Lie Algebras ◽  
Universal Algebra ◽  
Automorphism Groups ◽  
Endomorphism Semigroup ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Inner Automorphism ◽  
Groups Of Automorphisms ◽  
Inner Automorphisms

Let U be a universal algebra. An automorphism α of the endomorphism semigroup of U defined by α(φ) = sφs-1 for a bijection s : U → U is called a quasi-inner automorphism. We characterize bijections on U defining such automorphisms. For this purpose, we introduce the notion of a pre-automorphism of U. In the case when U is a free universal algebra, the pre-automorphisms are precisely the well-known weak automorphisms of U. We also provide different characterizations of quasi-inner automorphisms of endomorphism semigroups of free universal algebras and reveal their structure. We apply obtained results for describing the structure of groups of automorphisms of categories of free universal algebras, isomorphisms between semigroups of endomorphisms of free universal algebras, automorphism groups of endomorphism semigroups of free Lie algebras etc.

scholarly journals The Endomorphism Semigroup of a Special Semigroup

1970 ◽  
Vol 32 (1) ◽  
pp. 55-60
Author(s):  
Subrata Majumdar ◽  
Mohd. Altab Hossain
Keyword(s):  
Endomorphism Semigroup ◽  
Direct Sums ◽  
Commutative Semigroups ◽  
Ams Classification ◽  
Academy Of Sciences

The endomorphism semigroup for a class of commutative semigroups, called special semigroups, will be studied their structures will be determined in some important cases. AMS Classification : 20 Keywords: Special semigroups, freeness, divisibility, direct sums, endomorphism, endomorphism semigroup. doi: 10.3329/jbas.v32i1.2442 Journal of Bangladesh Academy of Sciences, Vol. 32, No. 1, 55-60, 2008

scholarly journals Homomorphisms of near-rings of continuous real-valued functions

1996 ◽  
Vol 53 (3) ◽  
pp. 401-411
Author(s):  
K.D. Magill
Keyword(s):  
Compact Hausdorff Space ◽  
Topological Structure ◽  
Hausdorff Space ◽  
Additive Group ◽  
Continuous Functions ◽  
Endomorphism Semigroup ◽  
Real Numbers ◽  
Extensive Class ◽  
Ring Of Functions

For any topological near-ring (which is not a ring) whose additive group is the additive group of real numbers, we investigate the near-ring of all continuous functions, under the pointwise operations, from a compact Hausdorff space into that near-ring. Specifically, we determine all the homomorphisms from one such near-ring of functions to another and we show that within a rather extensive class of spaces, the endomorphism semigroup of the near-ring of functions completely determines the topological structure of the space.

scholarly journals Automorphisms of the endomorphism semigroup of a polynomial algebra

2011 ◽  
Vol 333 (1) ◽  
pp. 40-54 ◽  
Author(s):  
A. Belov-Kanel ◽  
R. Lipyanski
Keyword(s):  
Polynomial Algebra ◽  
Endomorphism Semigroup
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