In mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular E-semigroup.[1] The term orthodox semigroup was coined by T. E. Hall and presented in a paper published in 1969.[2][3] Certain special classes of orthodox semigroups had been studied earlier. For example, semigroups that are also unions of groups, in which the sets of idempotents form subsemigroups were studied by P. H. H. Fantham in 1960.[4]
- ^ J. Almeida, J.-É. Pin and P. Weil Semigroups whose idempotents form a subsemigroup updated version of Almeida, J.; Pin, J.-É.; Weil, P. (2008). "Semigroups whose idempotents form a subsemigroup". Mathematical Proceedings of the Cambridge Philosophical Society. 111 (2): 241. doi:10.1017/S0305004100075332. S2CID 6344747.
- ^ Hall, T. E. (1969). "On regular semigroups whose idempotents form a subsemigroup". Bulletin of the Australian Mathematical Society. 1 (2): 195–208. doi:10.1017/s0004972700041447.
- ^ Clifford, A. H.; Hofmann, K. H.; Mislove, M. W., eds. (1996). Semigroup Theory and Its Applications: Proceedings of the 1994 Conference Commemorating the Work of Alfred H. Clifford. Cambridge University Press. p. 70. ISBN 9780521576697.
- ^ P.H.H. Fantham (1960). "On the Classification of a Certain Type of Semigroup". Proceedings of the London Mathematical Society. 1: 409–427. doi:10.1112/plms/s3-10.1.409.