We consider maximal stable orders on semigroups that belong to a certain class of inverse semigroups of finite rank.
Article PDF
Similar content being viewed by others
References
E. S. Lyapin, “On maximal two-sided stable orders in semigroups,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 34, No. 3, 88–94 (1963).
V. D. Derech, “On maximal stable orders on certain biideal extensions of the Brandt semigroup,” in: Semigroups and Their Homomorphisms [in Russian], Leningrad (1991), pp. 12–18.
V. D. Derech, “Congruences of a permutable inverse semigroup of finite rank,” Ukr. Mat. Zh., 57, No. 4, 469–473 (2005).
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. 1, American Mathematical Society, Providence, RI (1964).
M. Petrich, Inverse Semigroups, Wiley, New York (1984).
B. M. Schein, “Completions, translational hulls and ideal extensions of inverse semigroups,” Czech. Math. J., 23, 575–610 (1973).
A. Nagy and P. R. Jones, “Permutative semigroups whose congruences form a chain,” Semigroup Forum, 69, No. 3, 446–456 (2004).
A. G. Kurosh, Lectures on General Algebra [in Russian], Nauka, Moscow (1973).
H. Hamilton, “Permutability of congruences on commutative semigroups,” Semigroup Forum, 10, No. 1, 55–66 (1975).
V. D. Derech, “Structure of a permutable Mann semigroup of finite rank,” Ukr. Mat. Zh., 58, No. 6, 742–746 (2006).
B. M. Schein, “Representation of ordered semigroups,” Mat. Sb., 65, No. 2, 188–197 (1964).
S. M. Goberstein, “Fundamental order relations on inverse semigroups and on their generalizations, ” Semigroup Forum, 21, 285–328 (1980).
V. Derech, “On permutable inverse semigroups of finite rank,” in: Abstracts of the Fifth International Algebraic Conference in Ukraine, Odessa (2005), p. 57.
Author information
Authors and Affiliations
Additional information
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1035–1041, August, 2008.
Rights and permissions
About this article
Cite this article
Derech, V.D. On maximal stable orders on an inverse semigroup of finite rank with zero. Ukr Math J 60, 1210–1217 (2008). https://doi.org/10.1007/s11253-009-0132-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0132-1