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引用次数: 2
摘要
本书简介:非交换格的扩展研究始于1949年,由理论和数学物理学家恩斯特·帕斯夸尔·乔丹(Ernst Pascual Jordan)开始,他是马克斯·波恩(Max Born)和维尔纳·卡尔·海森堡(Werner Karl Heisenberg)的同事。Jordan引入了非交换格作为可能适合包含量子世界逻辑的代数结构。非交换格的现代理论始于四十年后的1989年Jonathan Leech的论文《环中的偏格》。近年来,格和相关结构的非交换推广引起了人们的极大兴趣,从拟格到斜Heyting代数,新的思想和应用不断涌现。这种活动在某种程度上源于乔纳森·里奇在这一领域的研究计划的启动。本书共分七章,主要涵盖了斜格、拟格和拟格、环中幂等的斜格和斜布尔代数。因此,它是第一个研究专著,涵盖了由于这一新研究的非交换格的主要结果。它将作为一个有价值的研究生教科书的主题,以及一个方便的参考研究非交换代数。
Jonathan E. Leech: Noncommutative Lattices: Skew Lattices, Skew Boolean Algebras and Beyond
About the book: The extended study of non-commutative lattices was begun in 1949 by Ernst Pascual Jordan, a theoretical and mathematical physicist and co-worker of Max Born and Werner Karl Heisenberg. Jordan introduced noncommutative lattices as algebraic structures potentially suitable to encompass the logic of the quantum world. The modern theory of noncommutative lattices began forty years later with Jonathan Leech’s 1989 paper “Skew lattices in rings.” Recently, noncommutative generalizations of lattices and related structures have seen an upsurge in interest, with new ideas and applications emerging, from quasilattices to skew Heyting algebras. Much of this activity is derived in some way from the initiation of Jonathan Leech’s program of research in this area. The present book consists of seven chapters, mainly covering skew lattices, quasilattices and paralattices, skew lattices of idempotents in rings and skew Boolean algebras. As such, it is the first research monograph covering major results due to this renewed study of noncommutative lattices. It will serve as a valuable graduate textbook on the subject, as well as a handy reference to researchers of noncommutative algebras.