B. Albayrak, O. Givradze and G. Partenadze, Generating sets of the complete
semigroups of binary relations defined by semilattices of the class Sigma_2(X; 4),
Applied Mathematics, 9 (2018), 17-27.
G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its
Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-
Amsterdam, 1976.
Z. Avaliani and Sh. Makharadze, Maximal subgroups of some classes of semigroups
of binary relations, Georgian Math. J., 11(2) (2004), 203-208.
R. Chaudhuri and A. Mukherjea, Idempotent Boolean matrices, Semigroup
Forum, 21 (1980), 273-282.
A. H. Clifford, A proof of the Montague-Plemmons-Schein theorem on maximal
subgroups of the semigroup of binary relations, Semigroup Forum, 1 (1970),
272-275.
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Part
1, Mathematical Surveys, No. 7, Amer. Math. Soc., Providence, R.I., 1961.
H. M. Devadze, Generating sets of the semigroup of all binary relations in a
finite set, Dokl. Akad. Nauk BSSR, 12 (1968), 765-768.
Ya. I. Diasamidze, One-sided zeros of subsets of a semigroup of binary relations,
Ukrainian Math. J., 42(5) (1990), 532-535.
Ya. I. Diasamidze, One-sided units of a subset of a semigroup of binary relations,
Ukrainian Math. J., 42(8) (1990), 915-918.
Ya. I. Diasamidze, The structure of idempotent binary relations, Studies of
semigroups (Russian), Leningrad. Gos. Ped. Inst., Leningrad, (1990), 25-28.
Ya. I. Diasamidze, Right units of complete semigroups of binary relations defined
by complete X-semilattices generated by pairwise nonintersecting sets,
Bull. Georgian Acad. Sci., 166(1) (2002), 23-26.
Ya. I. Diasamidze, Right units of complete semigroups of binary relations, defined
by complete X-semilattices generated by chains, Bull. Georgian Acad.
Sci., 167(2) (2003), 197-199.
Ya. Diasamidze and Sh. Makharadze, Complete Semigroups of Binary Relations,
Kriter, Turkey, 2013.
Ya. I. Diasamidze, N. Aydin and A. Erdo˘gan, Generating set of the complete
semigroups of binary relations, Applied Mathematics, 7 (2016), 98-107.
O. Givradze, Some properties of semigroup BX(D), defined by semilattice of
1(X; 4) class, Bull. Georgian Acad. Sci., 167(1) (2003), 43-46.
O. Givradze, Y. Diasamidze and N. Tsinaridze, Generated sets of the complete
semigroup binary relations defined by semilattices of the finite chains, Trans.
A. Razmadze Math. Inst., 172 (2018), 378-387.
P. Hell and J. Ne˘set˘ril, Graphs and Homomorphisms, Oxford Lecture Series in
Mathematics and its Applications, Vol. 28, Oxford University Press, Oxford,
2004.
P. M. Higgins, Techniques of Semigroup Theory, with a foreword by G. B.
Preston, Oxford Science Publications, The Clarendon Press, Oxford University
Press, New York, 1992.
J. M. Howie, Fundamentals of Semigroup Theory, London Mathematical Society
Monographs, New Series, 12, Oxford Science Publications, The Clarendon
Press, Oxford University Press, New York, 1995.
W. Imrich, S. Klavˇzar and D. F. Rall, Topics in Graph Theory: Graphs and
Their Cartesian Product, A K Peters, Ltd., Wellesley, MA, 2008.
K. H. Kim and F. W. Roush, Inverses of Boolean matrices, Linear Algebra
Appl., 22 (1978), 247-262.
F. Klein-Barmen, ¨ Uber eine weitere verallgemeinerung des verbandsbegriffes,
Math. Z., 46 (1940), 472-480.
J. Konieczny, Reduced idempotents in the semigroup of Boolean matrices, J.
Symbolic Comput., 20 (1995), 471-482.
J. Konieczny, A proof of Devadze’s theorem on generators of the semigroup of
Boolean matrices, Semigroup Forum, 83(2) (2011), 281-288.
K. Kuratowski and A. Mostowski, Set Theory, with an Introduction to Descriptive
Set Theory, Translated from the 1966 Polish original, Second, completely
revised edition, Studies in Logic and the Foundations of Mathematics,
Vol. 86, North-Holland Publishing Co., Amsterdam-New York-Oxford; PWNPolish
Scientific Publishers, Warsaw, 1976.
D. B. McAlister, Homomorphisms of semigroups of binary relations, Semigroup
Forum, 3(2) (1971/72), 185-188.
R. McKenzie and B. M. Schein, Every semigroup is isomorphic to a transitive
semigroup of binary relations, Trans. Amer. Math. Soc., 349(1) (1997), 271-
285.
J. S. Montague and R. J. Plemmons, Maximal subgroups of the semigroup of
relations, J. Algebra, 13 (1969), 575-587.
C. Namnak and P. Preechasilp, Natural partial orders on the semigroup of
binary relations, Thai J. Math., 4(3) (2006), 39-50.
O. Ore, Theory of equivalence relations, Duke Math. J., 9 (1942), 573-627.
R. J. Plemmons and B. M. Schein, Groups of binary relations, Semigroup
Forum, 1 (1970), 267-271.
R. J. Plemmons and M. T. West, On the semigroup of binary relations, Pacific
J. Math. 35 (1970), 743-753.
G. B. Preston, Any group is a maximal subgroup of the semigroup of binary
relations on some set, Glasgow Math. J., 14 (1973), 21-24.
B. M. Schein, Regular elements of the semigroup of all binary relations, Semigroup
Forum, 13(2) (1976/77), 95-102.
B. M. Shain, Representation of semigroups by means of binary relations, Mat.
Sb. (N.S.), 60(102) (1963), 293-303.
T. Tamura, Operations on binary relations and their applications, Bull. Amer.
Math. Soc., 70(1) (1964), 113-120.
P. M. Whitman, Lattices, equivalence relations and subgroups, Bull. Amer.
Math. Soc., 52 (1946), 507-522.
K. A. Zaretskii, Regular elements of the semigroup of binary relations, Uspehi
Mat. Nauk, 17 (1962), 177-179.
K. A. Zaretskii, The semigroup of binary relations, Mat. Sb. (N.S.), 61(103)
(1963), 291-305.
B. Albayrak, O. Givradze and G. Partenadze, Generating sets of the complete
semigroups of binary relations defined by semilattices of the class Sigma_2(X; 4),
Applied Mathematics, 9 (2018), 17-27.
G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its
Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-
Amsterdam, 1976.
Z. Avaliani and Sh. Makharadze, Maximal subgroups of some classes of semigroups
of binary relations, Georgian Math. J., 11(2) (2004), 203-208.
R. Chaudhuri and A. Mukherjea, Idempotent Boolean matrices, Semigroup
Forum, 21 (1980), 273-282.
A. H. Clifford, A proof of the Montague-Plemmons-Schein theorem on maximal
subgroups of the semigroup of binary relations, Semigroup Forum, 1 (1970),
272-275.
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. Part
1, Mathematical Surveys, No. 7, Amer. Math. Soc., Providence, R.I., 1961.
H. M. Devadze, Generating sets of the semigroup of all binary relations in a
finite set, Dokl. Akad. Nauk BSSR, 12 (1968), 765-768.
Ya. I. Diasamidze, One-sided zeros of subsets of a semigroup of binary relations,
Ukrainian Math. J., 42(5) (1990), 532-535.
Ya. I. Diasamidze, One-sided units of a subset of a semigroup of binary relations,
Ukrainian Math. J., 42(8) (1990), 915-918.
Ya. I. Diasamidze, The structure of idempotent binary relations, Studies of
semigroups (Russian), Leningrad. Gos. Ped. Inst., Leningrad, (1990), 25-28.
Ya. I. Diasamidze, Right units of complete semigroups of binary relations defined
by complete X-semilattices generated by pairwise nonintersecting sets,
Bull. Georgian Acad. Sci., 166(1) (2002), 23-26.
Ya. I. Diasamidze, Right units of complete semigroups of binary relations, defined
by complete X-semilattices generated by chains, Bull. Georgian Acad.
Sci., 167(2) (2003), 197-199.
Ya. Diasamidze and Sh. Makharadze, Complete Semigroups of Binary Relations,
Kriter, Turkey, 2013.
Ya. I. Diasamidze, N. Aydin and A. Erdo˘gan, Generating set of the complete
semigroups of binary relations, Applied Mathematics, 7 (2016), 98-107.
O. Givradze, Some properties of semigroup BX(D), defined by semilattice of
1(X; 4) class, Bull. Georgian Acad. Sci., 167(1) (2003), 43-46.
O. Givradze, Y. Diasamidze and N. Tsinaridze, Generated sets of the complete
semigroup binary relations defined by semilattices of the finite chains, Trans.
A. Razmadze Math. Inst., 172 (2018), 378-387.
P. Hell and J. Ne˘set˘ril, Graphs and Homomorphisms, Oxford Lecture Series in
Mathematics and its Applications, Vol. 28, Oxford University Press, Oxford,
2004.
P. M. Higgins, Techniques of Semigroup Theory, with a foreword by G. B.
Preston, Oxford Science Publications, The Clarendon Press, Oxford University
Press, New York, 1992.
J. M. Howie, Fundamentals of Semigroup Theory, London Mathematical Society
Monographs, New Series, 12, Oxford Science Publications, The Clarendon
Press, Oxford University Press, New York, 1995.
W. Imrich, S. Klavˇzar and D. F. Rall, Topics in Graph Theory: Graphs and
Their Cartesian Product, A K Peters, Ltd., Wellesley, MA, 2008.
K. H. Kim and F. W. Roush, Inverses of Boolean matrices, Linear Algebra
Appl., 22 (1978), 247-262.
F. Klein-Barmen, ¨ Uber eine weitere verallgemeinerung des verbandsbegriffes,
Math. Z., 46 (1940), 472-480.
J. Konieczny, Reduced idempotents in the semigroup of Boolean matrices, J.
Symbolic Comput., 20 (1995), 471-482.
J. Konieczny, A proof of Devadze’s theorem on generators of the semigroup of
Boolean matrices, Semigroup Forum, 83(2) (2011), 281-288.
K. Kuratowski and A. Mostowski, Set Theory, with an Introduction to Descriptive
Set Theory, Translated from the 1966 Polish original, Second, completely
revised edition, Studies in Logic and the Foundations of Mathematics,
Vol. 86, North-Holland Publishing Co., Amsterdam-New York-Oxford; PWNPolish
Scientific Publishers, Warsaw, 1976.
D. B. McAlister, Homomorphisms of semigroups of binary relations, Semigroup
Forum, 3(2) (1971/72), 185-188.
R. McKenzie and B. M. Schein, Every semigroup is isomorphic to a transitive
semigroup of binary relations, Trans. Amer. Math. Soc., 349(1) (1997), 271-
285.
J. S. Montague and R. J. Plemmons, Maximal subgroups of the semigroup of
relations, J. Algebra, 13 (1969), 575-587.
C. Namnak and P. Preechasilp, Natural partial orders on the semigroup of
binary relations, Thai J. Math., 4(3) (2006), 39-50.
O. Ore, Theory of equivalence relations, Duke Math. J., 9 (1942), 573-627.
R. J. Plemmons and B. M. Schein, Groups of binary relations, Semigroup
Forum, 1 (1970), 267-271.
R. J. Plemmons and M. T. West, On the semigroup of binary relations, Pacific
J. Math. 35 (1970), 743-753.
G. B. Preston, Any group is a maximal subgroup of the semigroup of binary
relations on some set, Glasgow Math. J., 14 (1973), 21-24.
B. M. Schein, Regular elements of the semigroup of all binary relations, Semigroup
Forum, 13(2) (1976/77), 95-102.
B. M. Shain, Representation of semigroups by means of binary relations, Mat.
Sb. (N.S.), 60(102) (1963), 293-303.
T. Tamura, Operations on binary relations and their applications, Bull. Amer.
Math. Soc., 70(1) (1964), 113-120.
P. M. Whitman, Lattices, equivalence relations and subgroups, Bull. Amer.
Math. Soc., 52 (1946), 507-522.
K. A. Zaretskii, Regular elements of the semigroup of binary relations, Uspehi
Mat. Nauk, 17 (1962), 177-179.
K. A. Zaretskii, The semigroup of binary relations, Mat. Sb. (N.S.), 61(103)
(1963), 291-305.
Dovgoshey, O. (2019). SEMIGROUPS GENERATED BY PARTITIONS. International Electronic Journal of Algebra, 26(26), 145-190. https://doi.org/10.24330/ieja.587041
AMA
Dovgoshey O. SEMIGROUPS GENERATED BY PARTITIONS. IEJA. Temmuz 2019;26(26):145-190. doi:10.24330/ieja.587041
Chicago
Dovgoshey, O. “SEMIGROUPS GENERATED BY PARTITIONS”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 145-90. https://doi.org/10.24330/ieja.587041.
EndNote
Dovgoshey O (01 Temmuz 2019) SEMIGROUPS GENERATED BY PARTITIONS. International Electronic Journal of Algebra 26 26 145–190.
IEEE
O. Dovgoshey, “SEMIGROUPS GENERATED BY PARTITIONS”, IEJA, c. 26, sy. 26, ss. 145–190, 2019, doi: 10.24330/ieja.587041.
ISNAD
Dovgoshey, O. “SEMIGROUPS GENERATED BY PARTITIONS”. International Electronic Journal of Algebra 26/26 (Temmuz 2019), 145-190. https://doi.org/10.24330/ieja.587041.
JAMA
Dovgoshey O. SEMIGROUPS GENERATED BY PARTITIONS. IEJA. 2019;26:145–190.
MLA
Dovgoshey, O. “SEMIGROUPS GENERATED BY PARTITIONS”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 145-90, doi:10.24330/ieja.587041.
Vancouver
Dovgoshey O. SEMIGROUPS GENERATED BY PARTITIONS. IEJA. 2019;26(26):145-90.