On Mal’cev’s Multiplication of Antivarieties of Algebraic Systems
In this paper it is proved that subantivarieties of an antivariety K form a semigroup with respect to Mal’cev’s multiplication whenever K is an antivariety of algebraic systems whose signature Ω contains only finite number of function symbols.We show that the condition of finiteness of the set of fu...
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| Published in | Lobachevskii journal of mathematics Vol. 39; no. 1; pp. 89 - 92 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper it is proved that subantivarieties of an antivariety K form a semigroup with respect to Mal’cev’s multiplication whenever K is an antivariety of algebraic systems whose signature Ω contains only finite number of function symbols.We show that the condition of finiteness of the set of function symbols from Ω is significant. Semigroups of subantivarieties of antivarieties of algebras are characterized. |
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| AbstractList | In this paper it is proved that subantivarieties of an antivariety K form a semigroup with respect to Mal’cev’s multiplication whenever K is an antivariety of algebraic systems whose signature Ω contains only finite number of function symbols.We show that the condition of finiteness of the set of function symbols from Ω is significant. Semigroups of subantivarieties of antivarieties of algebras are characterized. |
| Author | Kartashova, A. V. |
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| Cites_doi | 10.1090/S0002-9947-1978-0480230-6 10.1007/BF02219833 10.1007/BF02302476 10.1007/BF02572836 10.1007/BF02681563 10.1007/978-3-642-88599-0 |
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| Keywords | Antivariety Mal’cev’s multiplication algebraic system |
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| References | KohlerP.The semigroup of varieties of Brouwerian semilatticesTrans. Am. Math. Soc.197824133134248023010.1090/S0002-9947-1978-0480230-60389.06008 GorbunovV. A.KravchenkoA. V.Universal Horn classes and antivarieties of algebraic systemsAlgebra Logic200039111178231410.1007/BF026815630953.03038 MartynovaT. A.The groupoid of 0-reduced varieties of semigroupsSemigroup Forum19832624927469402410.1007/BF025728360546.20052 KartashovV. K.On groupoids of quasivarieties of unary algebrasUniversal Algebra and its Applications1999VolgogradVolgograd Gos. Ped. Univ. GorbunovV. A.Algebraic Theory of Quasivarieties1998New YorkConsultants Bureau0986.08001 Mal’cevA. I.Multiplication of classes of algebraic systemsSib. Math. J.1967825426721327610.1007/BF02302476 UrmanA. A.Groupoids of varieties of certain algebrasAlgebra Logic1969813814426230910.1007/BF022198330216.03301 NeumannH.Varieties of Groups1967Berlin, New YorkSpringer10.1007/978-3-642-88599-00149.26704 Mal’cevA. I.Algebraic Systems1970MoscowNauka A. I. Mal’cev (4611_CR1) 1970 V. A. Gorbunov (4611_CR2) 1998 H. Neumann (4611_CR5) 1967 V. A. Gorbunov (4611_CR3) 2000; 39 A. I. Mal’cev (4611_CR4) 1967; 8 V. K. Kartashov (4611_CR9) 1999 P. Kohler (4611_CR8) 1978; 241 A. A. Urman (4611_CR6) 1969; 8 T. A. Martynova (4611_CR7) 1983; 26 |
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| SubjectTerms | Algebra Analysis Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Multiplication Probability Theory and Stochastic Processes Symbols |
| Title | On Mal’cev’s Multiplication of Antivarieties of Algebraic Systems |
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