Amalgamation and inverse and regular semigroups
Author:
T. E. Hall
Journal:
Trans. Amer. Math. Soc. 246 (1978), 395406
MSC:
Primary 20M10
MathSciNet review:
515546
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Abstract: A method for proving the embeddability of semigroup amalgams is introduced. After providing necessary and sufficient conditions in terms of representations for the weak embeddability of a semigroup amalgam, it successfully deals with the embedding of inverse semigroup amalgams into inverse semigroups and the embedding of an amalgam of regular semigroups whose core is full in each member.
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H. Clifford, A structure theorem for orthogroups, J. Pure
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335–337. MR 0306366
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bands, J. Algebra 16 (1970), 204–217. MR 0265492
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E. Hall, On regular semigroups, J. Algebra 24
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T.
E. Hall, Orthodox semigroups, Pacific J. Math.
39 (1971), 677–686. MR 0306370
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T.
E. Hall, Free products with amalgamation of inverse
semigroups, J. Algebra 34 (1975), 375–385. MR 0382518
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, Representation extension and amalgamation for semigroups, Quart J. Math. Oxford (to appear).
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M. Howie, An introduction to semigroup theory, Academic Press
[Harcourt Brace Jovanovich, Publishers], LondonNew York, 1976. L.M.S.
Monographs, No. 7. MR 0466355
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Gerard
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Semigroup Forum 4 (1972), 95–123. MR 0296199
(45 #5260)
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G.
B. Preston, Matrix representations of semigroups, Quart. J.
Math. Oxford Ser. (2) 9 (1958), 169–176. MR 0099374
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G.
B. Preston, Inverse semigroups: some open questions,
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(Northern Illinois Univ., DeKalb, Ill., 1973) Northern Illinois Univ.,
DeKalb, Ill., 1973, pp. 122–139. MR 0414755
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 [13]
G.
B. Preston, Representations of inverse semigroups by onetoone
partial transformations of a set, Semigroup Forum 6
(1973), no. 3, 240–245; addendum, ibid. 8 (1974), no. 3, 277. MR 0376932
(51 #13107)
 [14]
G.
B. Preston, Free products amalgamating unitary subsemigroups,
Bull. Austral. Math. Soc. 15 (1976), no. 1,
117–124. MR 0424978
(54 #12936)
 [15]
, Free products amalgamating almost unitary subsemigroups (to be submitted).
 [1]
 A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Vols. 1, 2, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961, 1967.
 [2]
 A. H. Clifford, A structure theorem for orthogroups, J. Pure Appl. Algebra 8 (1976), 2350. MR 0409694 (53:13446)
 [3]
 D. G. FitzGerald, On inverses of products of idempotents in regular semigroups, J. Austral. Math. Soc. 13 (1972), 335337. MR 0306366 (46:5492)
 [4]
 T. E. Hall, On orthodox semigroups and uniform and antiuniform bands, J. Algebra 16 (1970), 204217. MR 0265492 (42:401)
 [5]
 , On regular semigroups, J. Algebra 24 (1973), 124. MR 0310098 (46:9201)
 [6]
 , Orthodox semigroups, Pacific J. Math. 39 (1971), 677686. MR 0306370 (46:5496)
 [7]
 , Free products with amalgamation of inverse semigroups, J. Algebra 34 (1975), 375385. MR 0382518 (52:3401)
 [8]
 , Representation extension and amalgamation for semigroups, Quart J. Math. Oxford (to appear).
 [9]
 J. M. Howie, An introduction to semigroup theory, London Math. Soc. Monographs no. 7, Academic Press, London and New York, 1976. MR 0466355 (57:6235)
 [10]
 Gerard Lallement, Structure theorems for regular semigroups, Semigroup Forum 4 (1972), 95123. MR 0296199 (45:5260)
 [11]
 G. B. Preston, Matrix representations of semigroups, Quart. J. Math. Oxford Ser. (2) 9 (1958), 169176. MR 0099374 (20:5814)
 [12]
 , Inverse semigroups: some open questions, Proc. Sympos. Inverse Semigroups and Their Generalizations, Northern Illinois Univ., De Kalb, Ill., 1973, pp. 122139. MR 0414755 (54:2848)
 [13]
 , Representations of inverse semigroups by onetoone partial transformations of a set, Semigroup Forum 6 (1973), 240245; Addendum, Semigroup Forum 8 (1974), 277. MR 0376932 (51:13107)
 [14]
 , Free products amalgamating unitary subsemigroups, Bull. Austral. Math. Soc. 15 (1976), 117124. MR 0424978 (54:12936)
 [15]
 , Free products amalgamating almost unitary subsemigroups (to be submitted).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197805155468
PII:
S 00029947(1978)05155468
Keywords:
Amalgamation,
inverse semigroups,
regular semigroups
Article copyright:
© Copyright 1978
American Mathematical Society
