| 乘法半群为矩形群的nil扩张的半环 |
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| 引用本文： | 蒲楠,李刚. 乘法半群为矩形群的nil扩张的半环[J]. 山东科学, 2019, 32(2): 125-129. DOI: 10.3976/j.issn.1002-4026.2019.02.016 |
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| 作者姓名： | 蒲楠 李刚 |
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| 作者单位： | 山东师范大学数学与统计学院,山东 济南 250014 |
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| 基金项目： | 国家自然科学基金(30471138,30370928) |
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| 摘 要： | 研究了加法半群为半格、乘法半群为矩形群的nil扩张的半环,从半环的子集出发构造乘法半群上的关系,得到H-为半环(Reg(S),+,·)上同余关系的充要条件,给出了矩形群的nil扩张转化为矩形带的nil扩张条件,并将矩形群的nil扩张性质推广到矩形带的nil扩张和矩形群上。
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| 关 键 词： | 半环 矩形群 GV半群 同余 nil扩张 |
| 收稿时间： | 2018-06-06 |
Semirings whose multiplicative semigroups are nilextensions of rectangular groups |
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| PU Nan,LI Gang. Semirings whose multiplicative semigroups are nilextensions of rectangular groups[J]. Shandong Science, 2019, 32(2): 125-129. DOI: 10.3976/j.issn.1002-4026.2019.02.016 |
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| Authors: | PU Nan LI Gang |
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| Affiliation: | Institute of Mathematics and Statistics, Shandong Normal University, Jinan 200514, China |
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| Abstract: | In this paper, we studied semirings in which additive semigroups were semilattices, multiplicative semigroups were nil extensions of rectangular groups. From the subsets of semirings, the relations on multiplicative semigroups were constructed. The necessary and sufficient condition for H- to be the congruence relation on semirings (Reg(S),+,·) was obtained. The conditions under which nil extension of a rectangular group could be transformed into nil extension of a rectangular band were given. The property of nil extension of rectangular groups was extended to the nil extension of rectangular bands and rectangular groups. |
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| Keywords: | semirings rectangular groups GV semigroups congruence nil extensions |
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