Congruence preserving operations on the ring ℤ p 3

Cyril Gavala; Miroslav Ploščica; Ivana Varga

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 4, page 519-535
  • ISSN: 0862-7959

Abstract

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We investigate the interval I ( p 3 ) in the lattice of clones on the ring ℤ p 3 between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.

How to cite

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Gavala, Cyril, Ploščica, Miroslav, and Varga, Ivana. "Congruence preserving operations on the ring $\mathbb {Z}_{p^3}$." Mathematica Bohemica 148.4 (2023): 519-535. <http://eudml.org/doc/299579>.

@article{Gavala2023,
abstract = {We investigate the interval $I(p^3)$ in the lattice of clones on the ring $\mathbb \{Z\}_\{p^3\}$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.},
author = {Gavala, Cyril, Ploščica, Miroslav, Varga, Ivana},
journal = {Mathematica Bohemica},
keywords = {congruence; clone; polynomial},
language = {eng},
number = {4},
pages = {519-535},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Congruence preserving operations on the ring $\mathbb \{Z\}_\{p^3\}$},
url = {http://eudml.org/doc/299579},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Gavala, Cyril
AU - Ploščica, Miroslav
AU - Varga, Ivana
TI - Congruence preserving operations on the ring $\mathbb {Z}_{p^3}$
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 519
EP - 535
AB - We investigate the interval $I(p^3)$ in the lattice of clones on the ring $\mathbb {Z}_{p^3}$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.
LA - eng
KW - congruence; clone; polynomial
UR - http://eudml.org/doc/299579
ER -

References

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