| 偏序集与偏序集代数的关系 |
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| 引用本文： | 陈仁迪.偏序集与偏序集代数的关系[J].新疆大学学报(理工版),1989,6(1):41-44. |
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| 作者姓名： | 陈仁迪 |
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| 作者单位： | 新疆大学数学系 |
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| 摘 要： | 本文研究偏序集与偏序集代数之间的关系.给出偏序集代数KI是Artin代数,Noether代数,半素代数以及素代数的充分必要条件;得到偏序集代数KI的Jacobson根J=KI~ ,并给出?的充分必要条件;最后,用偏序集代数KI的代数性质,给出偏序集I是格的充分必要条件.
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| 关 键 词： | 偏序集 代散 格 根 素 |
Relations Between Partial Ordered Sets And The Algebras Over Them |
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| Chen Rendi.Relations Between Partial Ordered Sets And The Algebras Over Them[J].Journal of Xinjiang University(Science & Engineering),1989,6(1):41-44. |
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| Authors: | Chen Rendi |
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| Institution: | Xinjiang University |
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| Abstract: | In this paper we study the relations between partial ordered sets and the algebras over them.Some sufficient and necessary conditions that an algebra over a partial ordered set is Artian,Noetherian,semi-prime or prime are given.The Jacobson radical of an algebra KI over a partial ordered set I is given,i.e.J=KI.We also give a necessary and sufficient condition for ? last,a necessary and sufficient condition of a partial ordered set I to be a lattice is given by the algebra properties of KI. |
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| Keywords: | partial ordered set algebra lattice radical prime |
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