| GCD-摹群条件下的半群环主理想升链条件 |
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| 引用本文： | 马晨江.GCD-摹群条件下的半群环主理想升链条件[J].三峡大学学报(自然科学版),2009,31(2):101-102. |
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| 作者姓名： | 马晨江 |
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| 作者单位： | 三峡大学,理学院,湖北,宜昌,443002 |
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| 摘 要： | 对交换半群环的主理想升链条件进行了讨论.在环是整环,半群S是交换无挠可消摹群,S中存在完全不可逆生成集的条件下得到一个关于半群环的主理想升链条件的充要条件.在交换摹群S是唯一分解的条件下证明了在S中存在完全不可逆生成集,由此得到交换无挠可消摹群是GCD-摹群的条件下关于半群环的主理想升链条件的充要条件.
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| 关 键 词： | 半群环 主理想升链条件 整环 交换无挠可消摹群 GCD-摹群 |
On Ascending Chain Condition on Principal Ideals of Semigroup Rings When Semigroups Are GCD-Monoids |
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| Ma Chenjiang.On Ascending Chain Condition on Principal Ideals of Semigroup Rings When Semigroups Are GCD-Monoids[J].Journal of China Three Gorges University(Natural Sciences),2009,31(2):101-102. |
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| Authors: | Ma Chenjiang |
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| Institution: | Ma Chenjiang (College of Science, China Three Gorges Univ. , Yichang 443002, China) |
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| Abstract: | The ascending chain condition on principal ideals（a, c. c. p. ） of semigroup rings is discussed. Under the semigroups are commutative torsion-free and cancellative monoids, a necessary and sufficient condition of a. c. c. p. of semigroup rings is obtained when there are complete non-reversible generating sets in the semigroups. And another necessary and sufficient condition of a, c. c.p. of semigroup rings is obtained under the condition that the rings are integral domains and commutative torsion-free and cancellative monoids are GCD- monoids. |
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| Keywords: | semigroup ring ascending chain condition on principal ideals integral domain commutative torsion-free and cancellative monoids GCD- monoids |
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