We describe the structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental.
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References
W. D. Munn, “Fundamental inverse semigroups,” Quart. J. Math. Oxford, 21, 157–170 (1970).
M. Petrich, Inverse Semigroups, Wiley, New York (1984).
V. D. Derech, “Congruences of a permutable inverse semigroup of finite rank,” Ukr. Mat. Zh., 57, No. 4, 469–473 (2005).
V. D. Derech, “On permutable congruences on antigroups of finite rank,” Ukr. Mat. Zh., 56, No. 3, 346–351 (2004).
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).
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups [Russian translation], Vols. 1, 2, Mir, Moscow (1972).
B. M. Schein, “Completions, translational hulls and ideal extensions of inverse semigroups,” Czech. Math. J., 23, 575–610 (1973).
V. D. Derech, “On maximal stable orders on an inverse semigroup of finite rank with zero,” Ukr. Mat. Zh., 60, No. 8, 1035–1041 (2008).
V. D. Derech, “Structure of a permutable Munn semigroup of finite rank,” Ukr. Mat. Zh., 58, No. 6, 742–746 (2006).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 52–60, January, 2009.
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Derech, V.D. Structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental. Ukr Math J 61, 57–70 (2009). https://doi.org/10.1007/s11253-009-0198-9
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DOI: https://doi.org/10.1007/s11253-009-0198-9