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Information × Registration Number 0219U100050, 0118U000998 , R & D reports Title Relatively free n-tuple semigroups popup.stage_title Head Zhuchok Anаtolii V., Доктор фізико-математичних наук Registration Date 11-01-2019 Organization State establishment „Luhansk Taras Shevchenko national Universityˮ popup.description2 A free product of arbitrary n-tuple semigroups is constructed, the notion of n-band of n-tuple semigroups is introduced and, in terms of this notion, the structure of the free product is described. A free commutative n-tuple semigroup of an arbitrary rank is constructed and one-generated free commutative n-tuple semigroups are characterized. The least commutative congruence on a free n-tuple semigroup is described. New examples of n-tuple semigroups are given. The cardinality of the free k-nilpotent n-tuple semigroup for a finite case is counted. It is shown that every abelian doppelsemigroup can be constructed from a left and right commutative semigroup and the free abelian doppelsemigroup is described. The least abelian congruence on the free doppelsemigroup is characterized, examples of abelian doppelsemigroups are given and conditions under which the operations of an abelian doppelsemigroup coincide are found. A free commutative trioid of rank 1 is constructed and it is proved that a free commutative trioid of rank n>1 is a subdirect product of a free commutative semigroup of rank n and a free commutative trioid of rank 1. The least commutative congruence, the least commutative dimonoid congruences and the least commutative semigroup congruence on a free trioid are characterized. Product Description popup.authors popup.nrat_date 2020-04-02 Close