TERNARY ∗-BANDS ARE GLOBALLY DETERMINED
A non-empty set \(S\) together with the ternary operation denoted by juxtaposition is said to be ternary semigroup if it satisfies the associativity property \(ab(cde)=a(bcd)e=(abc)de\) for all \(a,b,c,d,e\in S\). The global set of a ternary semigroup \(S\) is the set of all non empty subsets of \(S...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2023-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/429 |
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| author | Indrani Dutta Sukhendu Kar |
| author_facet | Indrani Dutta Sukhendu Kar |
| author_sort | Indrani Dutta |
| collection | DOAJ |
| description | A non-empty set \(S\) together with the ternary operation denoted by juxtaposition is said to be ternary semigroup if it satisfies the associativity property \(ab(cde)=a(bcd)e=(abc)de\) for all \(a,b,c,d,e\in S\). The global set of a ternary semigroup \(S\) is the set of all non empty subsets of \(S\) and it is denoted by \(P(S)\). If \(S\) is a ternary semigroup then \(P(S)\) is also a ternary semigroup with a naturally defined ternary multiplication. A natural question arises: "Do all properties of \(S\) remain the same in \(P(S)\)?"
The global determinism problem is a part of this question. A class \(K\) of ternary semigroups is said to be globally determined if for any two ternary semigroups \(S_1\) and \(S_2\) of \(K\), \(P(S_1)\cong P(S_2)\) implies that \(S_1\cong S_2\). So it is interesting to find the class of ternary semigroups which are globally determined. Here we will study the global determinism of ternary \(\ast\)-band. |
| format | Article |
| id | doaj-art-d9ead164b5634097bdda20960b848e25 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-d9ead164b5634097bdda20960b848e252025-08-20T03:58:54ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522023-07-019110.15826/umj.2023.1.005168TERNARY ∗-BANDS ARE GLOBALLY DETERMINEDIndrani Dutta0Sukhendu Kar1Jadavpur University, 188, Raja S. C. Mallick Road, Kolkata – 700032Jadavpur University, 188, Raja S. C. Mallick Road, Kolkata – 700032A non-empty set \(S\) together with the ternary operation denoted by juxtaposition is said to be ternary semigroup if it satisfies the associativity property \(ab(cde)=a(bcd)e=(abc)de\) for all \(a,b,c,d,e\in S\). The global set of a ternary semigroup \(S\) is the set of all non empty subsets of \(S\) and it is denoted by \(P(S)\). If \(S\) is a ternary semigroup then \(P(S)\) is also a ternary semigroup with a naturally defined ternary multiplication. A natural question arises: "Do all properties of \(S\) remain the same in \(P(S)\)?" The global determinism problem is a part of this question. A class \(K\) of ternary semigroups is said to be globally determined if for any two ternary semigroups \(S_1\) and \(S_2\) of \(K\), \(P(S_1)\cong P(S_2)\) implies that \(S_1\cong S_2\). So it is interesting to find the class of ternary semigroups which are globally determined. Here we will study the global determinism of ternary \(\ast\)-band.https://umjuran.ru/index.php/umj/article/view/429rectangular ternary band, involution ternary semigroup, involution ternary band, ternary \(\ast\)-band, ternary projection. |
| spellingShingle | Indrani Dutta Sukhendu Kar TERNARY ∗-BANDS ARE GLOBALLY DETERMINED Ural Mathematical Journal rectangular ternary band, involution ternary semigroup, involution ternary band, ternary \(\ast\)-band, ternary projection. |
| title | TERNARY ∗-BANDS ARE GLOBALLY DETERMINED |
| title_full | TERNARY ∗-BANDS ARE GLOBALLY DETERMINED |
| title_fullStr | TERNARY ∗-BANDS ARE GLOBALLY DETERMINED |
| title_full_unstemmed | TERNARY ∗-BANDS ARE GLOBALLY DETERMINED |
| title_short | TERNARY ∗-BANDS ARE GLOBALLY DETERMINED |
| title_sort | ternary ∗ bands are globally determined |
| topic | rectangular ternary band, involution ternary semigroup, involution ternary band, ternary \(\ast\)-band, ternary projection. |
| url | https://umjuran.ru/index.php/umj/article/view/429 |
| work_keys_str_mv | AT indranidutta ternarybandsaregloballydetermined AT sukhendukar ternarybandsaregloballydetermined |