Regular, inverse, and completely regular centralizers of permutations

Janusz Konieczny

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 2, page 179-186
  • ISSN: 0862-7959

Abstract

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For an arbitrary permutation σ in the semigroup T n of full transformations on a set with n elements, the regular elements of the centralizer C ( σ ) of σ in T n are characterized and criteria are given for C ( σ ) to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.

How to cite

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Konieczny, Janusz. "Regular, inverse, and completely regular centralizers of permutations." Mathematica Bohemica 128.2 (2003): 179-186. <http://eudml.org/doc/249210>.

@article{Konieczny2003,
abstract = {For an arbitrary permutation $\sigma $ in the semigroup $T_n$ of full transformations on a set with $n$ elements, the regular elements of the centralizer $C(\sigma )$ of $\sigma $ in $T_n$ are characterized and criteria are given for $C(\sigma )$ to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.},
author = {Konieczny, Janusz},
journal = {Mathematica Bohemica},
keywords = {semigroup of full transformations; permutation; centralizer; regular; inverse; completely regular semigroups; semigroups of full transformations; permutations; regular centralizers; inverse centralizers; completely regular semigroups},
language = {eng},
number = {2},
pages = {179-186},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regular, inverse, and completely regular centralizers of permutations},
url = {http://eudml.org/doc/249210},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Konieczny, Janusz
TI - Regular, inverse, and completely regular centralizers of permutations
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 2
SP - 179
EP - 186
AB - For an arbitrary permutation $\sigma $ in the semigroup $T_n$ of full transformations on a set with $n$ elements, the regular elements of the centralizer $C(\sigma )$ of $\sigma $ in $T_n$ are characterized and criteria are given for $C(\sigma )$ to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.
LA - eng
KW - semigroup of full transformations; permutation; centralizer; regular; inverse; completely regular semigroups; semigroups of full transformations; permutations; regular centralizers; inverse centralizers; completely regular semigroups
UR - http://eudml.org/doc/249210
ER -

References

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  1. 10.1017/S0017089500007011, Glasgow Math. J. 30 (1988), 41–57. (1988) Zbl0634.20034MR0925558DOI10.1017/S0017089500007011
  2. Fundamentals of Semigroup Theory, Oxford University Press, New York, 1995. (1995) Zbl0835.20077MR1455373
  3. 10.1017/S0017089599970301, Glasgow Math. J. 41 (1999), 45–57. (1999) Zbl0924.20049MR1689659DOI10.1017/S0017089599970301
  4. Semigroups of transformations commuting with idempotents, Algebra Colloq. 9 (2002), 121–134. (2002) Zbl1005.20046MR1901268
  5. Centralizers in the semigroup of partial transformations, Math. Japon. 48 (1998), 367–376. (1998) MR1664246
  6. On the permutability of mappings, Dokl. Akad. Nauk BSSR 7 (1963), 366–369. (Russian) (1963) MR0153609
  7. The order of the centralizer of a transformation, Dokl. Akad. Nauk BSSR 12 (1968), 596–598. (Russian) (1968) MR0237624
  8. 10.2140/pjm.1960.10.705, Pacific J. Math. 10 (1960), 705–711. (1960) Zbl0094.03203MR0115923DOI10.2140/pjm.1960.10.705

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