The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain

2012 ◽  
Vol 81 (1-2) ◽  
pp. 11-29 ◽  
Author(s):  
ILINKA DIMITROVA ◽  
VITOR H. FERNANDES ◽  
JORG KOPPITZ
Keyword(s):  
Finite Chain ◽  
Maximal Subsemigroups

The monoid of all orientation-preserving and extensive full transformations on a finite chain

2021 ◽  
pp. 2250105
Author(s):  
De Biao Li ◽  
Wen Ting Zhang ◽  
Yan Feng Luo
Keyword(s):  
Finite Chain ◽  
Generating Set ◽  
Maximal Subsemigroups ◽  
Idempotent Rank

Let [Formula: see text] be the monoid of all orientation-preserving and extensive full transformations on [Formula: see text] ordered in the standard way. In this paper, we determine the minimum generating set and the minimum idempotent generating set of [Formula: see text], and so the rank and the idempotent rank of [Formula: see text] are obtained. Moreover, we describe maximal subsemigroups and maximal idempotent generated subsemigroups of [Formula: see text] and completely obtain their classifications.

Critical Problem for codes over finite chain rings

2021 ◽  
Vol 76 ◽  
pp. 101900
Author(s):  
Koji Imamura ◽  
Keisuke Shiromoto
Keyword(s):  
Finite Chain ◽  
Critical Problem ◽  
Finite Chain Rings

ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

2008 ◽  
Vol 01 (02) ◽  
pp. 189-202 ◽  
Author(s):  
I. Dimitrova ◽  
J. Koppitz
Keyword(s):  
Transformation Semigroups ◽  
Maximal Subsemigroups ◽  
Element Set

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

A New Derivation of Postgel Properties of Network Polymers

1976 ◽  
Vol 49 (5) ◽  
pp. 1219-1231 ◽  
Author(s):  
D. R. Miller ◽  
C. W. Macosko
Keyword(s):  
General Result ◽  
Crosslink Density ◽  
Polymer Network ◽  
Probability Generating Function ◽  
Finite Chain ◽  
Network Polymer ◽  
Network Polymers ◽  
Property Relations ◽  
Recursive Scheme ◽  
Effective Network

Abstract The probability of a finite or dangling chain on an ideal polymer network has been derived by a simple recursive scheme. In contrast to the method of Dobson and Gordon, probability generating function formalism is not required. The general result, Equations (21), and its specific solutions, Equations (23), (24), and (30), give the finite chain probability as a function of reactant type and extent of polymerization. They cover most of the important types of network forming polymerizations. From the finite chain probability, useful property relations such as sol fraction, crosslink density, and the number of elastically effective network chains are developed. Because of their simplicity, we expect these relations to be further developed and applied to network polymer property measurements.

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