- 作者: 方源
- 作者服務機構: 國立成功大學應用數學研究所
- 中文摘要: 設S=(Z, A, δ)為一群半自動機,此處Z, A為群,δ:Z×A→Z為一傳遞函數。當G為群,M(G)={f: G→G}在函數加法及合成下自然構成一個近環。吾人稱M(Z)之子近環N(S)為一句法近環(Syntactic near-ring)。若N(S)由恆等函數 及所有 (a A)所產生成,此處 :Z→Z via =δ(q,a) q Z,因此 (方程式無法摘錄) 。設 為三階對稱群, 為所有由 至 之自同態所構成之集合,E( )為 元素加法產生之自同態近環。本文之目的乃研究s與N(S)間之互交作用。在本篇論文中,吾人證明了下列一極重要之結果: (方程式無法摘錄) , (方程式無法摘錄) ( ),此處S=( , ,δ)且 (方程式無法摘錄)
- 英文摘要: Let (方程式無法摘錄) be a group-semiautomaton where Z, A are groups and (方程式無法摘錄) is a transitionfunction. Let G be a group and M(G)={f:G→G}the transformation near-ring of all mappings from Ginto itself under the operations of mapping addition and composition. The subnear-ring N(S) of M(Z)generated by the identity mapping and all (方程式無法摘錄) where (方程式無法摘錄) is called thesyntactic near-ring of S. Thus, (方程式無法摘錄) and (方程式無法摘錄) Here we let be the symmetric group ofdegree three,EndS3 the set of all endomorphisms of S3 and E(S3) the endomorphism near-ring generatedadditively by EndS3. The purpose of this paper is to study the interplay between S and N(S). In thispaper we have shown a very interesting result that (方程式無法摘錄) and (方程式無法摘錄) where (方程式無法摘錄) with (方程式無法摘錄) 1980 mathematics subject classification (Amer.Math.Soc.):Primary 16A76.
- 中文關鍵字: monold; semiautomaton; automaton; group-semiautomaton; near-ring; endomorphism near-ring; syntactic near-ring
- 英文關鍵字: --