The potential relation and amalgamation bases for finite semigroups
Authors:
T. E. Hall and Mohan S. Putcha
Journal:
Proc. Amer. Math. Soc. 95 (1985), 361364
MSC:
Primary 20M10
MathSciNet review:
806071
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Abstract: Let be a finite semigroup, . When does there exist a finite semigroup containing such that in ? This problem was posed to the second named author by John Rhodes in 1974. We show here that if , are regular, then such a semigroup exists if and only if either in , or and . We use this result to show that analgamation bases for the class of finite semigroups have linearly ordered classes.
 [1]
A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Math. Surveys, I and II, Amer. Math. Soc., Providence, R. I., 1961 and 1967.
 [2]
T.
E. Hall, On the natural ordering of \cal𝐽classes and of
idempotents in a regular semigroup, Glasgow Math. J.
11 (1970), 167–168. MR 0269761
(42 #4656)
 [3]
T.
E. Hall, Free products with amalgamation of inverse
semigroups, J. Algebra 34 (1975), 375–385. MR 0382518
(52 #3401)
 [4]
T.
E. Hall, Representation extension and amalgamation for
semigroups, Quart. J. Math. Oxford Ser. (2) 29
(1978), no. 115, 309–334. MR 509697
(80a:20084), http://dx.doi.org/10.1093/qmath/29.3.309
 [5]
, Inverse and regular semigroups and amalgamation: a brief survey, Symposium on Regular Semigroups, De Kalb, Illinois, 1979, pp. 4979.
 [6]
J.
M. Howie, An introduction to semigroup theory, Academic Press
[Harcourt Brace Jovanovich, Publishers], LondonNew York, 1976. L.M.S.
Monographs, No. 7. MR 0466355
(57 #6235)
 [7]
John
Rhodes, Some results on finite semigroups, J. Algebra
4 (1966), 471–504. MR 0201546
(34 #1428)
 [1]
 A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Math. Surveys, I and II, Amer. Math. Soc., Providence, R. I., 1961 and 1967.
 [2]
 T. E. Hall, On the natural ordering of classes and of idempotents in a regular semigroup, Glasgow Math. J. 11 (1970), 167168. MR 0269761 (42:4656)
 [3]
 , Free products with amalgamation of inverse semigroups, J. Algebra 34 (1975), 375385. MR 0382518 (52:3401)
 [4]
 , Representation extension and amalgamation for semigroups, Quart. J. Math. Oxford Ser. (2) 29 (1978), 309334. MR 509697 (80a:20084)
 [5]
 , Inverse and regular semigroups and amalgamation: a brief survey, Symposium on Regular Semigroups, De Kalb, Illinois, 1979, pp. 4979.
 [6]
 J. M. Howie, An introduction to semigroup theory, London Math. Soc. Monographs 7, Academic Press, London, 1976. MR 0466355 (57:6235)
 [7]
 J. Rhodes, Some results on finite semigroups, J. Algebra 4 (1966), 471504. MR 0201546 (34:1428)
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DOI:
http://dx.doi.org/10.1090/S00029939198508060714
PII:
S 00029939(1985)08060714
Article copyright:
© Copyright 1985
American Mathematical Society
