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 -