On algebraic geometry over completely simple semigroups

Document Type : Research Paper

Author

Sobolev Institute of Mathematics

Abstract

We study equations over completely simple semigroups and describe the coordinate semigroups of irreducible algebraic sets for such semigroups.

Keywords

Main Subjects


[1] G. Baumslag, A. Miasnikov and V. N. Remeslennikov, Algebraic geometry over groups, Trends in Math. , Int. Conf.
Algorithmic problems in groups and semigroups (Lincoln, NE, May 1116, 1998), Birkhauser Boston, Boston, MA
(2000) 35{50.
[2] A. H. Clifford, The free completely regular semigroup on a set, J. Algebra , 59 (1979) 434{451.
[3] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups I, Providence, Amer. Math. Soc. , (1961).
[4] E. Daniyarova, A. Miasnikov and V. Remeslennikov, Uni cation theorems in algebraic geometry, Algebra Discrete
Math. , 1 (2008) 80{111.
[5] E. Daniyarova, A. Miasnikov and V. Remeslennikov, Algebraic geometry over algebraic structures I I: Fundations, J.
Math. Sci. , 185 (2012) 389{416.
[6] T. Harju, J. Karhumaki and M. Petrich, Compactness of systems of equations on completely regular semigroups ,
Structures in Logic and Computer Science, Lecture Notes in Comput. Sci., 1261, Springer, Berlin, 1997 268{280.
[7] P. R. Jones, Completely simple semigroups: free pro ducts, free semigroups and varieties, Proc. Roy. Soc. Edinburgh
Sect. A , 88 (1981) 293{313.
[8] A. Myasnikov and V. Remeslennikov, Algebraic geometry over groups I I: Logical foundations, J. Algebra , 234 (2000)
225{276.
[9] V. V. Rasin, Free completely simple semigroups, (Russian), Matem. Zapiski (Sverd lovsk) , (1979) 140{151.
[10] V. V. Rasin, On the lattice of varieties of completely simple semigroups, Semigroup Forum , 17 (1979) 113{122
  • Receive Date: 16 April 2016
  • Revise Date: 31 August 2017
  • Accept Date: 01 September 2017
  • Published Online: 01 June 2019