| 1. | Generalizations of finitely generated submodules
模的推广 |
| 2. | Group - graded rings of half - simple modules with finitely generated modules
有限生成半单分次模情形的群分次环 |
| 3. | A criterion theorem of having no finite coverings for a finitely generated module m over a semisimple ring r is given
对半单环上有限生成左模给出一个无有限覆盖的判定定理。 |
| 4. | Theorem 4 . 2 finite c * ( pq ) - group g is soluble . theorem 4 . 4 if g is finitely generated and c * ( n ) - group , then g is polycyclic group
4若有限生成的可解群g是c ” （ ）群，则g是多重循环群 |
| 5. | In the last section the author define and study finitely generated coreduced left goren - stein flat modules on n - gorenstein and left perfect rings
第四部分我们研究了n - gorenstein 、左完全环上有限生成的上约化的gorenstein平坦左r -模。 |
| 6. | We get some useful characters of right a - module , and find an index set ( q ) , q = 1 - 1a , is a system of finitely generated projec - tive generators of gr - ( a , ) for some - graded rings . results , we give the definition of semigroup gr - faithfully balanced
第二部分，对于半群我们给出如下定义：得到了半群分次右模上的一些性质，找到了半群分次右模的有限生成投射生成子，其中，并定义了半群分次?忠实?平衡模。 |
| 7. | 11 aubry p , lazard d , maza m m . on the theory of triangular sets . journal of symbolic computation , 1999 , : 105 - 124 . 12 bouziane d , rody a kandri , mahat arouf h . unmixed - dimensional decomposition of a finitely generated perfect differential ideal
这一方法在图像压缩计算机视觉计算机图形学智能cad sat问题求解一阶逻辑推理信息安全编码数控技术机器人等高技术领域与物理力学化学天文学中若干问题的研究中得到成功应用。 |
| 8. | At fist we can conclude that kernels of the flat cover of a finitely gener - ated coreduced gorenstein flat module is also a finitely generated coreduced gorenstein flat module . moreover , the flat cover of the former ( the first gorenstein flat module ) is the flat envelope of the latter
首先我们由它的平坦盖就可得到核也是有限生成的上约化gon stein平坦模，并且它的平坦盖正好是核的平坦包；类似地，它的平坦包的上核也是有限生成的上约化的gorenstein平坦模，且它的平坦包是其上核的平坦盖 |
| 9. | Similarly , cokernels of the flat envelope of a finitely gener - ated coreduced gorenstein flat module is also a finitely generated coreduced gorenstein flat module , moreover the flat envelope of the former is the flat cover of the latter . and then we prove that over these rings , in quotient categories mod every finitely generated module has a finitely generated coreduced gorenstein flat preenvelope , and its two such preenvelopes are isomorphic
接着证明了这类环上每个模的极小平坦分解式的合冲模从第n个起都是有限生成的上约化的gorenstein平坦模，最后证明了在这类环上，商范畴dlaa中每个有限生y成模都有有限生成的上约化的gorenstein平坦包，并且这种盖在同构意义下是唯一的 |
