| 实UFD上的几类格序矩阵代数 |
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| 引用本文： | 白先龙,李斐. 实UFD上的几类格序矩阵代数[J]. 首都师范大学学报(自然科学版), 2011, 32(5): 1-6 |
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| 作者姓名： | 白先龙 李斐 |
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| 作者单位： | 首都师范大学数学科学学院,北京,100048 |
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| 摘 要： | 设Z是整数环,如果(Mn(Z),+,×,≥)(n≥3)是一个格序环,则它也可以作为Z模有一个含有n2个元的vl-基B.如果B中恰有n2-n-1个幂零元时,本文确定了Mn(Z)上的格序代数的同构类型(见定理3.4),而且我们将该结果推广到实数中一般的唯一因子分解环R上(见定理3.5).另外,如果在Mn(R)上的一个格序代...
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| 关 键 词： | 格序 格序代数 矩阵 |
Several Kinds of Lattice-ordered Matrix Algebra Over Real UFD |
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| Bai Xianlong,Li Fei. Several Kinds of Lattice-ordered Matrix Algebra Over Real UFD[J]. Journal of Capital Normal University(Natural Science Edition), 2011, 32(5): 1-6 |
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| Authors: | Bai Xianlong Li Fei |
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| Affiliation: | Bai Xianlong Li Fei(School of Mathematical Sciences,Capital Normal University,Beijing 100048) |
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| Abstract: | Let Z be the ring of integer numbers.If(Mn(R),+,×,NFDA1)(n3) is a lattice-ordered ring,then it has n2 elements with vl-basis as Z-module.If there are exactly n2-n-1 nilpotent elements in B,we give the type of isomorphism class of lattice ordered matrix algebra on Mn(Z)(see theorem 3.4),and the result is generalized to the unique factorization rings in real number field(see theorem 3.5).Morever,if the lattice order of Mn(R) is independent,then it is isomorphic to the some special lattice ordered matrix algebra(see theorem 3.8). |
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| Keywords: | lattice order lattice-ordered algebra matrix. |
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