Completely Regular Semigroup Varieties: Applications and Advanced Techniques
暫譯: 完全正則半群類別：應用與進階技術
Petrich, Mario, Reilly, Norman R.
- 出版商: Springer
- 出版日期: 2025-02-05
- 售價: $1,940
- 貴賓價: 9.5 折 $1,843
- 語言: 英文
- 頁數: 201
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031488245
- ISBN-13: 9783031488245
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相關分類:
離散數學 Discrete-mathematics
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商品描述
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Polák's theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Polák's theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
商品描述(中文翻譯)
本書介紹了完全正規半群理論領域的進一步發展和應用，首先應用 Polák 定理來獲得各種核心類別的詳細描述，包括所有帶的核心類別的 K 類覆蓋。接著，利用完全正規半群的變種格的模塊性這一重要性質來分析各種主要子格。隨後研究了格上的某些重要完全同餘；群、局部和核心關係。下一章專門討論某些自由對象及相關的字問題。在半群理論中有許多構造。在完全正規半群的變種理論中發揮重要作用的構造在此上下文中被呈現。將每個變種映射到其與帶的變種的交集的映射是完全正規半群變種格到帶變種格的完全回縮，因此誘導出一個完全同餘，其中每個類別都有一個最大成員。然後在 Polák 定理的許多應用的幫助下，研究由這些最大成員生成的子格。本書以一個關於這個子格結構的迷人猜想作結。
作者簡介
Mario Pettrich received his PhD from the University of Washington in 1961 and held positions in many universities across Austria, Canada, France, Germany, Italy, Portugal, Spain, the UK and the US, including Pennsylvania State University, University of Western Ontario, University of Vienna, University of St Andrews, Simon Fraser University, and University of Montpellier. He was a Founding Editor of Semigroup Forum. Dr. Petrich has published over 260 articles, seven monographs and one Research Note. The principal focus of his work was in the field of semigroup theory.
Norman Reilly received his PhD from Glasgow University in 1965 and has held positions at Glasgow University, Tulane University, and Simon Fraser University. Dr. Reilly has published over 100 articles and two books. He is a long time editor of Semigroup Forum and the International Journal of Algebra and Computation. The focus of his research has been on algebraic systems, including ordered algebraic systems, witha main focus on the theory of semigroups.
作者簡介(中文翻譯)
馬里奧·佩特里奇（Mario Pettrich）於1961年在華盛頓大學獲得博士學位，並在奧地利、加拿大、法國、德國、義大利、葡萄牙、西班牙、英國和美國的多所大學任職，包括賓夕法尼亞州立大學、西安大略大學、維也納大學、聖安德魯斯大學、西門菲莎大學和蒙彼利埃大學。他是《半群論壇》（Semigroup Forum）的創始編輯之一。佩特里奇博士已發表超過260篇文章、七本專著和一篇研究報告。他的主要研究重點是半群理論（semigroup theory）領域。
諾曼·瑞利（Norman Reilly）於1965年在格拉斯哥大學獲得博士學位，並在格拉斯哥大學、杜蘭大學和西門菲莎大學任職。瑞利博士已發表超過100篇文章和兩本書籍。他是《半群論壇》（Semigroup Forum）和《國際代數與計算期刊》（International Journal of Algebra and Computation）的長期編輯。他的研究重點是代數系統（algebraic systems），包括有序代數系統，主要集中在半群理論上。
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