两个保序全变换半群的直积上的主同余

The Principal Congruences on the Direct Products of Two Order-preserving Full Transformation Semigroups

令T_(n)为X_(n)={1,2,…,n}上的全变换半群,且令O_(n)={α∈T_(n)|■x,y∈X_(n),x≤y■x_(α)≤y_(α)}为Tn的保序全变换子半群,文章将刻画直积O_(m)×O_(n)上的主同余.

Let T_(n) be a full transformation semigroup on X_(n)={1,2,…,n}, and let O_(n)={α∈T_(n)|■x,y∈X_n,x≤y■x_(α)≤y_(α)} bean order-preserving full transformation subsemigroup of T_(n), this paper will describe the principal congruences on the direct products of O_(m)×O_(n).