Bi-regular rings and the ideal lattice isomorphisms
Bi-regular rings and the ideal lattice isomorphisms
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双正则环和理想晶格同构
DOI：
10.1090/s0002-9939-1955-0067094-x
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发表时间：
1955
期刊：
影响因子：
--
通讯作者：
D. Morrison
中科院分区：
文献类型：
--
作者：
D. Morrison
1.幂等布尔环RO及其理想。在本文中，符号R用来表示环，RO用来表示R中心的幂等元的集合。如果a，bER0，我们用a(b=(a-b)2来定义符号(D)。定理1.2 RO是关于幂等加法和乘法运算的布尔环(称为R的幂等布尔环)。如果e是R的单位，那么e就是RO的单位。证据。证明只是对布尔环的公设成立这一事实的验证。读者可以提供细节。引理1.如果i是R的理想，且Ecio，则e在R的中心。
1. The idempotent Boolean ring, RO, and its ideals. The symbol R will be used throughout this paper to represent a ring and RO to represent the set of idempotent elements in the center of R. If a, bER0, we define the symbol (D by a ( b = (a - b) 2. The operation (D will be called idempotent addition. THEOREM 1.2 RO is a Boolean ring (called the idempotent Boolean ring of R) with respect to the operations of idempotent addition and multiplication. If e is a unit for R, then e is a unit for RO. PROOF. The proof is merely the verification of the fact that the postulates for a Boolean ring are satisfied. The reader may supply the details. LEMMA 1. If I is an ideal of R, and eCIO, then e is in the center of R.