THE FINITE BASIS PROBLEM FOR FINITE SEMIGROUPS

 VOLKOV M. V.
 Department of Mathematics and Mechanics Ural State University
Search this Article
Author(s)

 VOLKOV M. V.
 Department of Mathematics and Mechanics Ural State University
Journal

 Scientiae Mathematicae japonicae

Scientiae Mathematicae japonicae 53(1), 171199, 20010101
References: 92

1
 <no title>

ALMEIDA J.
Finite Semigroups and Universal Algebra, 1994
Cited by (1)

2
 Strict regular *semigroups

AUINGER K.
Proc. Conf. on Semigroups with Applications, 190204, 1992
Cited by (1)

3
 Free subsemigroups in soluble groups

BELYAEV V. V.
Investigations in Modem Algebra, 1318, 1981
Cited by (1)

4
 On the structure of abstract algebras

BIRKHOFF G.
Proc. Cambridge Philos. Soc. 31, 433454, 1935
Cited by (1)

5
 <no title>

BURRIS S.
A course in universal algebra, 1981
Cited by (4)

6
 <no title>

CLIFFORD A. H.
The Algebraic Theory of Semigroups I, 1961
Cited by (2)

7
 <no title>

CLIFFORD A. H.
The Algebraic Theory of Semigroups II, 1967
Cited by (2)

8
 Partial crosssections of symmetric inverse semigroups

COWAN D. F.
Int. J. Algebra and Computation 5, 259287, 1995
Cited by (1)

9
 Regular semigroups with involution

DRAZIN M. P.
Proc. Symp. on Regular Semigroups, 2946, 1979
Cited by (1)

10
 Pseudovarieties generated by transformation semigroups

HIGGINS P. M.
Semigroups and Their Applications, Including Semigroup Rings, 8594, 1999
Cited by (1)

11
 <no title>

HOWIE J. M.
Fundamentals of Semigroup Theory, 1995
Cited by (3)

12
 Base non finie de varietes

IRASTORZA C.
Theor. Aspects Comput. Sci. 2nd ann. Symp., 180186, 1985
Cited by (1)

13
 Two examples in varieties of monoids

ISBELL J. R.
Proc. Cambridge Philos. Soc. 68, 265266, 1970
Cited by (1)

14
 Small Semigroup Related Structures with Infinite Properties

JACKSON M.
Ph. D. thesis, Univ. of Tasmania, 1999
Cited by (1)

15
 Algorithmic problems in varieties

KHARLAMPOVICH O. G.
Int. J. Algebra and Computation 5, 379602, 1995
Cited by (1)

16
 Representations of events in nerve nets and finite automata

KLEENE S. C.
Automata Studies [Annals of Math. Studies 34], 1956
Cited by (1)

17
 Bases of identities of varieties of inverse semigroups

KLEIMAN E. I.
Sibirsk. Mat. Zh. 20, 760777, 1979
Cited by (1)

18
 <no title>

KLEIMAN E. I.
Two theorems on combinatorial varieties of inverse semigroups 12, 1980
Cited by (1)

19
 On a pseudovariety generated by a finite semigroup

KLEIMAN I.
Algebraic Systems and Their Varieties, 4042, 1982
Cited by (1)

20
 On a basis of the product of varieties of groups

KLEIMAN E. I.
Izv. Akad. Nauk SSSR, Ser. Mat. 37, 9597, 1973
Cited by (1)

21
 The number of semigroups of order n

KLEITMAN D. J.
Proc. Amer. Math. Soc. 55, 227232, 1976
Cited by (1)

22
 Note on the number of monoids of order n

KOUBEK V.
Comment. Math. Univ. Carolin. 26, 309314, 1985
Cited by (1)

23
 <no title>

LALLEMENT G.
Semigroups and Combinatorial Applications, 1979
Cited by (1)

24
 An example of a finite semigroup without irreducible identity basis in the class of completely 0simple semigroups

MASHEVITZKY G. I.
Uspekhi Mat. Nauk 38(2), 211213, 1983
Cited by (1)

25
 On a finite basis problem for universal positive formulas

MASHEVITZKY G. I.
Algebra Universalis 35, 124140, 1996
Cited by (1)

26
 On the finite basis problem for left hereditary systems of semigroup identities

MASHEVITZKY G. I.
Semigroups, Automata and Languages, 167181, 1996
Cited by (1)

27
 Tarski's finite basis problem is undercidable

MCKENZIE R.
Int. J. Algebra and Computation 6, 1996
Cited by (1)

28
 On varieties and lattices of varieties of semigroups

MEL'NIK I. I.
Investigations on Algebra 2, 4757, 1970
Cited by (1)

29
 Nilpotent shifts of varieties

MEL'NIK I. I.
Mat. Zametki 14, 703712, 1973
Cited by (1)

30
 Nondiscernible properties of finite systems of identity relations

MURSKII V. L.
Dokl. Akad. Nauk SSSR 196, 520522, 1971
Cited by (1)

31
 On the number of kelement algebras with one binary operation without a finite basis of identities

MURSKII V. L.
Problemy Kibernet. 35, 527, 1979
Cited by (1)

32
 <no title>

MYHILL J.
Finite automata and the representation of events, 112137, 1957
Cited by (1)

33
 Decision Problems for Equational Theories of Semigroups and General Algebras

PERKINS P.
Ph. D. thesis, Univ. of California, 1966
Cited by (1)

34
 Basic questions for general algebras

PERKINS P.
Algebra Universalis 19, 1623, 1984
Cited by (1)

35
 On almost simple semigroup identities

POLLAK Gy.
Semiegroups [Colloq. Math. Soc. Janos Bolyai, 39], 287323, 1985
Cited by (1)

36
 Varieties of orthodox Cloffordian semigroups

RASIN V. V.
Izv. Vyssh. Uchebn. Zaved. Mat. 11, 8285, 1982
Cited by (1)

37
 The finite basis problem for the pseudovariety

REPNITSKII V. B.
Proc. Royal Soc. Edinburgh 128A, 661669, 1998
Cited by (1)

38
 Semigroup Quasivarieties

SAPIR M. V.
Ph. D. thesis, Ural State Univ., 1983
Cited by (1)

39
 Inherently nonfinitely based finite semigroups

SAPIR M. V.
Mat. Sb. 133(2), 154166, 1987
Cited by (1)

40
 Problems of Burnside type and the finite basis property in varieties of semigroups

SAPIR M. V.
Izv. Akad. Nauk SSSR, Ser. Mat. 51, 319340, 1987
Cited by (1)

41
 Sur la propriete de base finie pour les pseudovarietes de semigroups finis

SAPIR M. V.
R. Acad. Sci. Paris (Ser. I) 306, 795797, 1988
Cited by (1)

42
 Identities of finite inverse semigroups

SAPIR M. V.
Int. J. Algebra and Computation 3, 115124, 1993
Cited by (1)

43
 Identities of Finite Semigroups and Related Questions

SAPIR O.
Ph. D. thesis, Univ. of Nebraska, 1997
Cited by (1)

44
 Semigroups, Chap. IV

SHEVRIN L. N.
General Algebra 2, 11191, 1991
Cited by (1)

45
 <no title>

SHNEERSON L. M.
On varieties generated by onerelator semigroups and monoids 32, 1984
Cited by (1)

46
 Identities of semigroups

SHEVRIN L. N.
Izv. Vyssh. Uchebn. Zaved. Mat. 11, 347
Cited by (1)

47
 <no title>

SHEVRIN L. N. (ed.)
The Sverdlovsk Notebook. Unsolved Problems of the Theory of Semigroups, 1979
Cited by (1)

48
 <no title>

SHEVRIN L. N. (ed.)
The Sverdlovsk Notebook. Unsolved Problems of the Theory of Semigroups, 1989
Cited by (1)

49
 Eduational logic and equational theories of algebras

TARSKI A.
Contributions to Mathematical Logic: Proc. Logic Colloq., 275288, 1968
Cited by (1)

50
 Wreath products of varieties, and semiArchimedean semigroup varieties

TISHCHENKO A. V.
Trudy Moskov. Mat. Obshch. 57, 218238, 1996
Cited by (1)

51
 <no title>

TORLOPOVA N. G.
On semigroups of rank 2 23, 1982
Cited by (1)

52
 An identity basis of the 5element Brandt semigroup

TRAHTMAN A. N.
Investigations in Modern Algebra, 147149, 1981
Cited by (1)

53
 <no title>

TRAHTMAN A. N.
Graphs of identities of a completely 0simple 5element semigroup, preprint 6, 1981
Cited by (1)

54
 Certain finite nonfinitely based semigroups

TRAHTMAN A. N.
Investigations of Algebraic Systems by Properties of Their Subsystems, 128131, 1987
Cited by (1)

55
 A sixelement semigroup generating a variety with uncountably many subvarieties

TRAHTMAN A. N.
Algebraic Systems and Their Varieties, 138143, 1988
Cited by (1)

56
 Finiteness of identity bases of 5element semigroups

TRAHTMAN A. N
Semigroups and Their Homomorphisms, 7697, 1991
Cited by (1)

57
 On the join of varieties

VOLKOV M. V.
Simon Stevin 58, 311317, 1984
Cited by (1)

58
 On the identity bases of Brandt semigroups

VOLKOV M. V.
Investigations of Algebraic Systems by Properties of Their Subsystems, 3842, 1985
Cited by (1)

59
 On finite basedness of semigroup varieties

VOLKOV M. V.
Mat. Zametki 45(3), 1223, 1989
Cited by (1)

60
 On a class of semigroup pseudovarieties without finite pseudoidentity basis

VOLKOV M. V.
Int. J. Algebra and Computation 5, 127135, 1995
Cited by (1)

61
 Covers in the lattices of semigroup varieties and pseudovarieties

VOLKOV M. V.
Semigroups, Automata and Languages, 263280, 1996
Cited by (1)

62
 The finite basis problem for the pseudovariety PO

VOLKOV M. V.
Semigroups and Applications, 239257, 1998
Cited by (1)

63
 The finite basis problem for finite semigroups: a survey

VOLKOV M. V.
Semigroups, 2000
Cited by (1)

64
 HFB property and structure of semigroups

VOLKOV M. V.
Contributions to General Algebra 6, 303310, 1988
Cited by (1)

65
 Blocking sets of terms

ZIMIN A. I.
Mat. Sb. 119, 363375, 1982
Cited by (1)

66
 Equations for pseudovarieties

ALMEIDA J.
Formal Properties of Finite Automata and Applications, 148164, 1989
Cited by (1)

67
 On iterated semidirect products of finite semilattices

ALMEIDA J.
J. Algebra 142, 239254, 1991
DOI Cited by (1)

68
 On identity bases of epigroup varieties

AUINGER K.
J. Algebra 220, 437448, 1999
DOI Cited by (1)

69
 Equations and monoid varieties of dotdepth one and two

BLANCHETSADRI F.
Theor. Comput. Sci. 123, 239258, 1994
Cited by (1)

70
 The laws of finite pointed groups

BRYANT R. M.
Bull. London Math. Soc. 14, 119123, 1984
DOI Cited by (2)

71
 Almeida's generalized variety problem

CHURCHILL G.
J. Algebra 196, 499519, 1997
DOI Cited by (1)

72
 A note on varieties of semiprime rings with semigroup identities

GOLUBCHIK I. Z.
J. Algebra 54, 4245, 1978
DOI Cited by (1)

73
 Completely 0simple semigroups and their associated graphs and groups

HOUGHTON C. H.
Semigroup Forum 14, 4168, 1977
DOI Cited by (1)

74
 Finite semigroups whose varieties have uncountably many subvarieties

JACKSON M.
J. Algebra 228, 512535, 2000
DOI Cited by (1)

75
 <no title>

KADOUREK J.
Semigroup Forum 44, 5378, 1992
DOI Cited by (1)

76
 On bases of identities of Brandt semigroups

KLEIMAN E. I.
Semigroup Forum 13, 209218, 1977
DOI Cited by (1)

77
 On finitely based groups and nonfinitely based quasivarieties

LAWRENCE J.
J. Algebra 203, 111, 1998
DOI Cited by (1)

78
 Quasiidentities of finite semigroups and symbolic dynamics

MARGOLIS S. W.
Isr. J. Math. 92, 317331, 1995
DOI Cited by (1)

79
 On bases of completely simple semigroups identities

MASHEVITZKY G. I.
Semigroup Forum 30, 6776, 1984
DOI Cited by (1)

80
 Completely simple and completely 0simple semigroup identities

MASHEVITZKY G. I.
Semigroup Forum 37, 253264, 1988
DOI Cited by (1)

81
 Matrix rank 1 semigroup identities

MASHEVITZKY G. I.
Comm. Algebra 22, 35533562, 1994
DOI Cited by (1)

82
 On the finite basis problem for completely 0simple semigroup identities

MASHEVITZKY G. I.
Semigroup Forum 59, 197219, 1999
DOI Cited by (1)

83
 Identical relations in finite groups

OATES S.
J. Algebra 1, 1139, 1965
DOI Cited by (2)

84
 Unsolvable problems for equational theories

PERKINS P.
Notre Dame J. Formal Logic 8, 175185, 1967
DOI Cited by (1)

85
 Bases for equational theories of semigroups

PERKINS P.
J. Algebra 11, 298314, 1969
DOI Cited by (2)

86
 On the varieties of Cliffordian semigroups

RASIN V. V.
Semigroup Forum 23, 201220, 1981
DOI Cited by (1)

87
 On Cross semigroup varieties and related questions

SAPIR M. V.
Semigroups Forum 42, 345364, 1991
DOI Cited by (1)

88
 On the join fo semigroup varieties with the variety of commutative semigroups

SAPIR M. V.
Proc. Amer. Math. Soc. 120, 345348, 1994
DOI Cited by (1)

89
 Finitely based words

SAPIR O.
Int. J. Algebra and Computation 10, 457480, 2000
DOI Cited by (1)

90
 A remark on functionally free algebras

TARSKI A.
Amer. J. Math. 47, 163165, 1946
DOI Cited by (2)

91
 The finite basis problem for semigroups of order less than six

TRAHTMAN A. N.
Semigroup Forum 27, 387389, 1983
DOI Cited by (1)

92
 The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups

TROTTER P. G.
Semigroup Forum 52, 8391, 1996
DOI Cited by (1)