On the subsemigroup generated by ordered idempotents of a regular semigroup

Anjan Kumar Bhuniya; Kalyan Hansda

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 2, page 205-211
  • ISSN: 1509-9415

Abstract

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An element e of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup g e n e r a t e d b y t h e s e t o f a l l o r d e r e d i d e m p o t e n t s o f a r e g u l a r o r d e r e d s e m i g r o u p S . I f S i s a r e g u l a r o r d e r e d s e m i g r o u p t h e n is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.

How to cite

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Anjan Kumar Bhuniya, and Kalyan Hansda. "On the subsemigroup generated by ordered idempotents of a regular semigroup." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 205-211. <http://eudml.org/doc/276485>.

@article{AnjanKumarBhuniya2015,
abstract = {An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup \[ generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is a regular ordered semigroup then \] is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.},
author = {Anjan Kumar Bhuniya, Kalyan Hansda},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {ordered regular; ordered inverse; ordered idempotent; downward closed; completely regular},
language = {eng},
number = {2},
pages = {205-211},
title = {On the subsemigroup generated by ordered idempotents of a regular semigroup},
url = {http://eudml.org/doc/276485},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Anjan Kumar Bhuniya
AU - Kalyan Hansda
TI - On the subsemigroup generated by ordered idempotents of a regular semigroup
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 2
SP - 205
EP - 211
AB - An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup \[ generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is a regular ordered semigroup then \] is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.
LA - eng
KW - ordered regular; ordered inverse; ordered idempotent; downward closed; completely regular
UR - http://eudml.org/doc/276485
ER -

References

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