TY - JOUR
AU - Howie, J. M.
AB - SUBSEMIGROUPS OF AMALGAMATED FREE PRODUCTS OF SEMIGROUPS By J. M. HOWIE [Received 12 July 1962] 1. LET {S ; i el} be a (finite or infinite) family of semigroups, and suppose that there exist a semigroup U and a monomorphism (p \U-^-S for each i i i in I. Then U<Pi is a subsemigroup of 8 ; we shall denote it by U^ The semigroups TJ are all isomorphic: specifically, tp^ = <pj cpj is an iso- morphism between C^ and Uj. In a previous paper, the author showed that if, for each i in / , the subsemigroup t^ is 'almost unitary' in S then 11^*$^, the free product i} of the semigroups #$ amalgamating U, contains an isomorphic copy S * of each S and an isomorphic copy U* of U such that 8 * n #,* = U* if t t i^j ((4) Theorems 2.3 and 3.3). In § 2 it is shown that if £7^ is unitary (and hence almost unitary) in $< for each i in I, then £7* is a unitary subsemigroup of 11^*$^ In § 3 an example is constructed to show that the theorem in § 2 cannot be generalized to 
TI - Subsemigroups of Amalgamated Free Products of Semigroups
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-13.1.672
DA - 1963-01-01
UR - https://www.deepdyve.com/lp/wiley/subsemigroups-of-amalgamated-free-products-of-semigroups-bnZJo4aCdS
SP - 672
EP - 686
VL - s3-13
IS - 1
DP - DeepDyve
ER -