半群PD(n,r)的秩和相关秩

doi:10.6040/j.issn.1671-9352.0.2019.922

摘要/Abstract

摘要： 设自然数n≥3, PDn是有限链［n］上的保距部分一一奇异变换半群。PD(n,r)={α∈PDn:|im(α)|≤r}(0≤r≤n-1)是半PDn的双边理想。通过对半群PDn的秩为r的元素的分析,获得了半群PD(n,r)的极小生成集和秩。进一步确定了当0≤l≤r时,半群PD(n,r)关于其理想PD(n,l)的相关秩。

关键词: 保距, 部分一一奇异变换半群, 生成集, 秩, 相关秩

Abstract: Let PDn be the semigroup of all distance-preserving partial one-to-one singular transformations on a finite-chain ［n］(n≥3), and let PD(n,r)={α∈PDn:|im(α)|≤r}(0≤r≤n-1)be the two-sided ideal of the semigroup PDn. By analyzing the elements with rank r of the semigroup PDn, the minimal generating set and rank of the semigroup PD(n,r)are obtained. Furthermore, the relative rank of the semigroup PD(n,r)with respect to its ideal PD(n,l)is determined for 0≤l≤r.

Key words: distance-preserving, partial one-to-one singular transformation semigroup, generating set, rank, relative rank

中图分类号:

O152.7

张前滔,罗永贵,赵平. 半群PD(n,r)的秩和相关秩[J]. 《山东大学学报(理学版)》, 2020, 55(10): 63-70.

ZHANG Qian-tao, LUO Yong-gui, ZHAO Ping. Rank and relative rank of the semigroup PD(n,r)[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 63-70.

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