Amalgamation and inverse and regular semigroups

Hall, T. E.

doi:10.1090/S0002-9947-1978-0515546-8

Amalgamation and inverse and regular semigroups
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Trans. Amer. Math. Soc. 246 (1978), 395-406 Request permission

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.

References

The algebraic theory of semigroups

A. H. Clifford, A structure theorem for orthogroups, J. Pure Appl. Algebra 8 (1976), no. 1, 23–50. MR 409694, DOI 10.1016/0022-4049(76)90021-9
D. G. Fitz-Gerald, On inverses of products of idempotents in regular semigroups, J. Austral. Math. Soc. 13 (1972), 335–337. MR 0306366, DOI 10.1017/S1446788700013756
T. E. Hall, On orthodox semigroups and uniform and antiuniform bands, J. Algebra 16 (1970), 204–217. MR 265492, DOI 10.1016/0021-8693(70)90025-6
T. E. Hall, On regular semigroups, J. Algebra 24 (1973), 1–24. MR 310098, DOI 10.1016/0021-8693(73)90150-6
T. E. Hall, Orthodox semigroups, Pacific J. Math. 39 (1971), 677–686. MR 306370, DOI 10.2140/pjm.1971.39.677
T. E. Hall, Free products with amalgamation of inverse semigroups, J. Algebra 34 (1975), 375–385. MR 382518, DOI 10.1016/0021-8693(75)90164-7

Representation extension and amalgamation for semigroups

J. M. Howie, An introduction to semigroup theory, L. M. S. Monographs, No. 7, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0466355
Gerard Lallement, Structure theorems for regular semigroups, Semigroup Forum 4 (1972), 95–123. MR 296199, DOI 10.1007/BF02570776
G. B. Preston, Matrix representations of semigroups, Quart. J. Math. Oxford Ser. (2) 9 (1958), 169–176. MR 99374, DOI 10.1093/qmath/9.1.169
G. B. Preston, Inverse semigroups: some open questions, Proceedings of a Symposium on Inverse Semigroups and their Generalisations (Northern Illinois Univ., DeKalb, Ill., 1973) Northern Illinois Univ., DeKalb, Ill., 1973, pp. 122–139. MR 0414755
G. B. Preston, Representations of inverse semigroups by one-to-one partial transformations of a set, Semigroup Forum 6 (1973), no. 3, 240–245; addendum, ibid. 8 (1974), no. 3, 277. MR 376932, DOI 10.1007/BF02389127
G. B. Preston, Free products amalgamating unitary subsemigroups, Bull. Austral. Math. Soc. 15 (1976), no. 1, 117–124. MR 424978, DOI 10.1017/S0004972700036820

Free products amalgamating almost unitary subsemigroups