保序且保距严格部分一一变换半群

The Semigroup of all Order-preserving and Distance-preserving Strictly Partial One-one Transformations

设[n]={1,2,···,n}为自然序集,ODI_(n)为所有保序且保距严格部分一一变换所构成的半群.证明了ODI_(n)的秩为n,并得到了ODI_(n)的极大逆子半群的完全分类.

Let [n]={1,2,···,n} be a natural order set, and denote by ODIn the semigroup consisting of all order-preserving and distance-preserving strictly partial one-one transformations. It is shown that the rank of ODI_(n)is n and obtained classification of maximal inverse subsemigroup of ODI_(n)completely.