近预量子及其在星与半星运算以及理想与模系统中的应用
环与代数
2010-11-19 v3 交换代数
摘要
我们证明了量子与预量子理论的一种推广为星运算、半星运算、半素运算、理想系统和模系统的理论提供了一个非交换且非结合的抽象理想理论框架，反之，后者的理论也激发了量子与预量子理论中的新结果。应用包括：预凝聚预量子和乘法半格的表示定理；简单交换量子和简单乘法格的刻画；在预凝聚预量子上构造小于给定核的最大有限核；在整环上构造扩展给定星运算的最小半星运算；以及两个可能有用的、针对素特征非诺特交换环的紧闭包定义。
引用
@article{arxiv.1002.3451,
title = {Near prequantales and applications to star and semistar operations and ideal and module systems},
author = {Jesse Elliott},
journal= {arXiv preprint arXiv:1002.3451},
year = {2010}
}
备注
This paper has been withdrawn by the author because the paper since submission has been changed and edited substantially, with many additions, omissions, and corrections. A new paper with a similar title will be submitted in the next couple of months