TY - JOUR
T1 - On diagonal acts of monoids
AU - Robertson, Edmund Frederick
AU - Ruskuc, Nikola
AU - Thomson, MR
PY - 2001/2
Y1 - 2001/2
N2 - It is proved that the monoid R-N of all partial recursive functions of one variable is finitely generated, and that R-N x R-N is a cyclic (left and right) R-N-act (under the natural diagonal actions s(alpha, b) = (s alpha, sb), (alpha, b)s = (alphas, bs)). We also construct a finitely presented monoid S such that S x S is a cyclic left and right S-act, and study further interesting properties of diagonal acts and their relationship with power monoids.
AB - It is proved that the monoid R-N of all partial recursive functions of one variable is finitely generated, and that R-N x R-N is a cyclic (left and right) R-N-act (under the natural diagonal actions s(alpha, b) = (s alpha, sb), (alpha, b)s = (alphas, bs)). We also construct a finitely presented monoid S such that S x S is a cyclic left and right S-act, and study further interesting properties of diagonal acts and their relationship with power monoids.
UR - http://www.scopus.com/inward/record.url?scp=0035256299&partnerID=8YFLogxK
U2 - 10.1017/S0004972700019225
DO - 10.1017/S0004972700019225
M3 - Article
SN - 1755-1633
VL - 63
SP - 167
EP - 175
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 1
ER -