| 广义双循环半群和Jones半群 |
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| 引用本文： | 喻秉钧,蒋启芬.广义双循环半群和Jones半群[J].数学进展,2000,29(3):235-244. |
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| 作者姓名： | 喻秉钧 蒋启芬 |
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| 作者单位： | 四川师范大学数学系, 成都,四川, 610066, 中国 |
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| 基金项目： | 国家自然科学基金(No.
19671063)和四川省教委重点科研基金项目. |
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| 摘 要： | 本文刻画了广义双循环半群Ｂｎ＝〈ａ，ｂ｜ａ＾ｎｂ＝１〉和Ｊｏｎｅｓ半群Ａｎ＝〈ａ，ｂ｜ａ＾ｎ＋１ｂ＝ａ〉（ｎ≥１）的结构；证明了每个Ａｎ都具有Ｐ．Ｒ．Ｊｏｎｅｓ所发现的半群Ａ＝〈ａ，ｂ｜ａ＾２ｂ＝ａ〉的所有重要性质，特别地，证明了Ａｎ，Ａｍ可互相嵌入，从而得到：第三个Ｄ－非平凡的无幂等元「０－」单半群若不含Ｃ＝〈ａ，ｂ｜ａ＾２ｂ＝ａ，ａｂＴ＾２＝ｂ〉，则必含每个Ａｎ或它们的对偶，作为推论，每人广义
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| 关 键 词： | 广义双循环半群 Jones半群 无幂等元同余 |
| 修稿时间： | 1998年8月20日 |
Generalized Bicyclic Semigroups and Jones Semigroups |
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| Yu Bingjun,Jiang Qifen.Generalized Bicyclic Semigroups and Jones Semigroups[J].Advances in Mathematics,2000,29(3):235-244. |
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| Authors: | Yu Bingjun Jiang Qifen |
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| Abstract: | The generalized bicyclic semigroups B and the Jones semigroups are characterized in this paper. It is proved that each of A. possesses all the important properties discovered by P. R. Jones for In parlicular, it is proved that A. and Am are mutually embeddable. Thus every nnontrivial O-] simple semigroup without idempotents, if contains no contains each A. or its dual. As a consequence, generalized bicyclic semigroups divide such O-] simple sermgroups |
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| Keywords: | generalized bicyclic semigroups Jones spmigroups quasilength of a word idempotent-free congruence minimal idempotent-free quotient |
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