| J-Boolean like环 |
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| 引用本文： | 秦蕊. J-Boolean like环[J]. 杭州师范学院学报(自然科学版), 2013, 0(5): 413-417 |
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| 作者姓名： | 秦蕊 |
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| 作者单位： | 杭州师范大学理学院,浙江杭州310036 |
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| 摘 要： | 本文首先引进了Boolean-like环的一类新的扩张J-Boolean like环,即对任意环R中元素a,b都有（a-a2）（b-b2）∈J（R）,这里J（R）为环R的Jacobson根,则环R称为J-Boolean like环.证明了两个定理分别为（1）设D是一个环,C是D的一个子环,R[D,C]是一个J-Boolean like环（a）C,D是J-Boolean like环,（b）J2（C）J（D）.（2）如果B/J（B）是Boolean环,并且B[i]={a＋bi｜i2=ui＋η,a,b,u,η∈B},那么B[i]是J-Boolean like环当且仅当uη∈J（B）.
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| 关 键 词： | Boolean环 Boolean-like环 J-Boolean like环 Jacobson根 R[D,C]环 |
J-Boolean Like Ring |
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| QIN Rui. J-Boolean Like Ring[J]. Journal of Hangzhou Teachers College(Natural Science), 2013, 0(5): 413-417 |
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| Authors: | QIN Rui |
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| Affiliation: | QIN Rui (College of Science, Hangzhou Normal University, Hangzhou 310036, China) |
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| Abstract: | This paper defined a new expansion of Boolean-like rings that was a ring R was called J-Boolean like ring when a, b in any ring R satisfied the condition that （a--a2 ） （b--b2 ）∈ J（R） and J（R） was the Jacobson radical of ring R. Two theorems was also proved. Let D be a ring, C is a subring of D, then RID,C] is a J-Boolean like ring if and only if （a）C,D are J-Boolean like rings, （b）J2 （C）J（D）. If B/J（B） is a Boolean ring, and BEi]= {a＇q-biliz =uiq-v,a,b,η∈B } , then B[＇i] is a J-Boolean like ring if and only if uη∈（B）. |
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| Keywords: | Boolean ring Boolean-like ring J-Boolean like ring Jacobson radical R[D, C-]ring |
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