Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$
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 o...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2023-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/148/4/mb148_4_7.pdf |
| _version_ | 1827696765992697856 |
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| author | Cyril Gavala Miroslav Ploščica Ivana Varga |
| author_facet | Cyril Gavala Miroslav Ploščica Ivana Varga |
| author_sort | Cyril Gavala |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T12:54:59Z |
| format | Article |
| id | doaj.art-4303e287ae604ff3bfd3e8f55d81595b |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-03-10T12:54:59Z |
| publishDate | 2023-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-4303e287ae604ff3bfd3e8f55d81595b2023-11-21T12:00:13ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362023-12-01148451953510.21136/MB.2022.0155-21MB.2022.0155-21Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$Cyril GavalaMiroslav PloščicaIvana VargaWe 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.http://mb.math.cas.cz/full/148/4/mb148_4_7.pdf congruence clone polynomial |
| spellingShingle | Cyril Gavala Miroslav Ploščica Ivana Varga Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ Mathematica Bohemica congruence clone polynomial |
| title | Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ |
| title_full | Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ |
| title_fullStr | Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ |
| title_full_unstemmed | Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ |
| title_short | Congruence preserving operations on the ring $\mathbb{Z}_{p^3}$ |
| title_sort | congruence preserving operations on the ring mathbb z p 3 |
| topic | congruence clone polynomial |
| url | http://mb.math.cas.cz/full/148/4/mb148_4_7.pdf |
| work_keys_str_mv | AT cyrilgavala congruencepreservingoperationsontheringmathbbzp3 AT miroslavploscica congruencepreservingoperationsontheringmathbbzp3 AT ivanavarga congruencepreservingoperationsontheringmathbbzp3 |