模上的Groebner基

Groebner Bases for Modules

Groebner基是代数中基本的计算工具之一.本文通过将Groebner基在理想上的一条性质推广到模上,来研究模上的Groebner基.首先证明模上的Groebner基的几个等价刻画;然后提出模上的Groebner基的一条性质;最后,根据所提的性质以及等价刻画,讨论Rm中元素f,g的s-多项式的性质.结果表明,所提的性质对研究模上的Groebner基是有意义的.

Groebner base is one of the basically computational tools in algebraic theory. In this paper, we study the Groebner bases for modules by extending a property of Groebner bases for ideals. Firstly, we prove some equivalent statements about the Groebner bases for modules. Then, we present a property of Groebner bases for modules. Finally, based on this property and the given equivalent conditions, we discuss a property of the s - polynomial of the elementsf, g in R^m. In a word, these results show that it is interesting to study Groebner ha- ses through the presented property.