Prime ideal theory for general algebras

被引：9
|
作者：
Erné, M [1 ]
机构：
[1] Univ Hannover, Dept Math, D-30167 Hannover, Germany
来源：
APPLIED CATEGORICAL STRUCTURES | 2000年 / 8卷 / 1-2期
关键词：
closure system; cm-lattice; distributive; ideal; locale; prime; quantale; radical; residuated; semiprime;
D O I：
10.1023/A:1008611926427
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).
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页码：115 / 144
页数：30
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