scholarly journals Regular order-preserving transformation semigroups

2000 ◽  
Vol 62 (3) ◽  
pp. 511-524 ◽  
Author(s):  
Yupaporn Kemprasit ◽  
Thawhat Changphas
Keyword(s):  
Finite Chain ◽  
Transformation Semigroups

The semigroup OT (X) of all order-preserving total transformations of a finite chain X is known to be regular. We extend this result to subchains of Z; and we characterise when OT (X) is regular for an interval X in R. We also consider the corresponding idea for partial transformations of arbitrary chains and posets.

scholarly journals On relative ranks of finite transformation semigroups with restricted range

2021 ◽  
Vol 73 (5) ◽  
pp. 617-626
Author(s):  
I. Dimitrova ◽  
J. Koppitz
Keyword(s):  
Restricted Range ◽  
Finite Chain ◽  
Transformation Semigroups ◽  
Relative Rank ◽  
Generating Sets ◽  
Finite Transformation

UDC 512.5 We determine the relative rank of the semigroup of all transformations on a finite chain with restricted range modulo the set of all orientation-preserving transformations in Moreover, we state the relative rank of the semigroup modulo the set of all order-preserving transformations in In both cases we characterize the minimal relative generating sets.  

scholarly journals On Divisors of Pseudovarieties Generated by Some Classes of Full Transformation Semigroups

2008 ◽  
Vol 15 (04) ◽  
pp. 581-588
Author(s):  
Vítor H. Fernandes
Keyword(s):  
Finite Chain ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Division Theorem

In this paper we present a division theorem for the pseudovariety of semigroups 𝖮𝖣 (𝖮𝖱) generated by all semigroups of order-preserving or order-reversing (orientation-preserving or orientation-reversing) full transformations on a finite chain.

scholarly journals Certain characterizations of varieties of bands

1988 ◽  
Vol 31 (2) ◽  
pp. 301-319 ◽  
Author(s):  
J. A. Gerhard ◽  
Mario Petrich
Keyword(s):  
Rectangular Band ◽  
Simple System ◽  
Left Zero ◽  
Green’S Relations ◽  
Transformation Semigroups ◽  
Lattice Of Varieties ◽  
Green's Relations ◽  
The World ◽  
New System

The lattice of varieties of bands was constructed in [1] by providing a simple system of invariants yielding a solution of the world problem for varieties of bands including a new system of inequivalent identities for these varieties. References [3] and [5] contain characterizations of varieties of bands determined by identities with up to three variables in terms of Green's relations and the functions figuring in a construction of a general band. In this construction, the band is expressed as a semilattice of rectangular bands and the multiplication is written in terms of functions among these rectangular band components and transformation semigroups on the corresponding left zero and right zero direct factors.

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
Sign in / Sign up

Export Citation Format

Share Document