Representations of semigroups and the translational hull of a regular Rees matrix semigroup

Petrich, Mario

doi:10.1090/S0002-9947-1969-0246984-3

Representations of semigroups and the translational hull of a regular Rees matrix semigroup
HTML articles powered by AMS MathViewer

by Mario Petrich PDF

Trans. Amer. Math. Soc. 143 (1969), 303-318 Request permission

References

Michael A. Arbib (ed.), Algebraic theory of machines, languages, and semigroups, Academic Press, New York-London, 1968. With a major contribution by Kenneth Krohn and John L. Rhodes. MR 0232875
I. E. Burmistrovič, Commutative bands of cancellative semigroups, Sibirsk. Mat. Ž. 6 (1965), 284–299 (Russian). MR 0173719
A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
L. M. Gluskīn, Semigroups and rings of endomorphisms of linear spaces, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 841–870 (Russian). MR 0143833
L. M. Gluskīn, Ideals of semigroups, Mat. Sb. (N.S.) 55 (97) (1961), 421–448 (Russian). MR 0139675
P. A. Grillet and Mario Petrich, Ideal extensions of semigroups, Pacific J. Math. 26 (1968), 493–508. MR 237686
Gérard Lallement and Mario Petrich, Irreducible matrix representations of finite semigroups, Trans. Amer. Math. Soc. 139 (1969), 393–412. MR 242973, DOI 10.1090/S0002-9947-1969-0242973-3
D. D. Miller and A. H. Clifford, Regular ${\scr D}$-classes in semigroups, Trans. Amer. Math. Soc. 82 (1956), 270–280. MR 78379, DOI 10.1090/S0002-9947-1956-0078379-0
Mario Petrich, The translational hull of a completely $0$simple semigroup, Glasgow Math. J. 9 (1968), 1–11. MR 229739, DOI 10.1017/S0017089500000239
Mario Petrich, Translational hull and semigroups of binary relations, Glasgow Math. J. 9 (1968), 12–21. MR 229740, DOI 10.1017/S0017089500000240
Mario Petrich, The semigroup of endomorphisms of a linear manifold, Duke Math. J. 36 (1969), 145–152. MR 238975
I. S. Ponizovskiĭ, Transitive representations by transformations of semi-groups of a certain class, Sibirsk. Mat. . 5 (1964), 896–903 (Russian). MR 0171866
N. R. Reilly, Bisimple $\omega$-semigroups, Proc. Glasgow Math. Assoc. 7 (1966), 160–167 (1966). MR 190252
B. M. Šaĭn, On the theory of generalized groups and generalized heaps, Theory of Semigroups and Appl. I (Russian), Izdat. Saratov. Univ., Saratov, 1965, pp. 286–324 (Russian). MR 0209385

Representation of a semigroup by transformations of a set

V. V. Vagner, Generalized groups, Doklady Akad. Nauk SSSR (N.S.) 84 (1952), 1119–1122 (Russian). MR 0048425
V. V. Vagner, Semigroups of partial mappings with a symmetric transitivity relation, Izv. Vysš. Učebn. Zaved. Matematika 1957 (1957), no. 1, 81–88 (Russian). MR 0160839