On characteristic properties of semigroups
Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P cha\-racteristic for a semigroup S∈ K if, up to isomorphism and anti-isomorphism, S is the only semigroup in K, which satisfies all the properties from Q. The set of properties P is call...
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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/154755 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On characteristic properties of semigroups / V.M. Bondarenko, Y.V. Zaciha // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 32-39. — Бібліогр.: 1 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P cha\-racteristic for a semigroup S∈ K if, up to isomorphism and anti-isomorphism, S is the only semigroup in K, which satisfies all the properties from Q.
The set of properties P is called char-complete for K if for any S∈ K the set of all properties P∈ P, which hold for the semigroup S, is characteristic for S.
We indicate a 7-element set of properties of semigroups which is a minimal char-complete setfor the class of semigroups of order 3. |
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