半群C F(n,r)的幂等元秩

doi:10.6040/j.issn.1671-9352.0.2023.111

摘要/Abstract

摘要： 设T_n是X_n={1,2,…,n}上的全变换半群,对任意1≤r≤n,令F_(n,r)={α∈T_n:iα=i, ∠i∈{1,2,…,r}},则F_(n,r)是T_n的子半群。本文将研究半群F_(n,r)的核C F_(n,r)=〈E(F_(n,r))〉,其中E(F_(n,r))={α∈F_(n,r):α²=α},通过对F_(n,r)幂等元的分析,得到半群C F_(n,r)的秩和幂等元秩都为((n-r)(n-r-1))/2+r(n-r)+1。

关键词: 变换半群, 核, 固定集, 幂等元秩

Abstract: Let T_n be the full transformation semigroup on X_n={1,2,…,n}. Let 1≤r≤n, putF_(n,r)={α∈T_n:iα=i, ∠i∈{1,2,…,r}},it is obvious that the semigroup F_(n,r) is subsemigroup of T_n. In the paper, we study the core(C F_(n,r))=〈E(F_(n,r))〉 of the semigroup F_(n,r), where E(F_(n,r))={α∈F_(n,r):α²=α}, by analyzing idempotents of the semigroup F_(n,r), we prove that the rank and idempotent rank of semigroup C F_(n,r) are both equal to ((n-r)(n-r-1))/2+r(n-r)+1.

Key words: transformation semigroup, core, fixed set, idempotent rank

中图分类号:

O152.7

龚何余,舒琴,赵平. 半群C F_(n,r)的幂等元秩[J]. 《山东大学学报(理学版)》, 2024, 59(10): 122-126.

GONG Heyu, SHU Qin, ZHAO Ping. On the rank of semigroup C F_(n,r)[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 122-126.

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