TY - JOUR
AU - Howie, J. M.
AB - EMBEDDING THEOREMS WITH AMALGAMATION FOR SEMIGROUPS! By J. M. HOWIE [Received 1 July 1961] 1. Introduction TH E following problem is considered. Let {S^, iel} be a family of semigroups, and suppose that there exists a semigroup U and a mono- morphism fa: U-+Si for each i in / . Ufa is a subsemigroup of ^ and will be denoted U . The U are all isomorphic, and faj = </>^"</>- is an t t ; isomorphism between U and Uj. We wish to find a semigroup T with the following properties: (a) There exist monomorphisms A^: S -^T (iel) such tha t u<j> \ = u<f>j Xj t t for all ueU and for all i,jel; that is, there exists a monomorphism A: U-+T which equals faX for all i in I. (b) S^oS^^UXiijEl^^j). I t is clear from (a) that ^A^n^A^E/A, and therefore (b) may be replaced by (b)' SiXiCiSjXjC UX. When such a T can be found, we shall say tha t 'the embedding [(S^; U] is possible'. I t is known (1) tha t this embedding is not always possible. It is also known that it is sometimes possible, for in the case when U 
TI - Embedding Theorems with Amalgamation for Semigroups†
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-12.1.511
DA - 1962-01-01
UR - https://www.deepdyve.com/lp/wiley/embedding-theorems-with-amalgamation-for-semigroups-DFJS00Howt
SP - 511
EP - 534
VL - s3-12
IS - 1
DP - DeepDyve
ER -