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 fractional ring 分式环(5)分式环的(3)
 分式环
 The question that how to determine a module M over a commutative ring R with invariant factors was discussed,and the result indicated that M was such an R-module if and only if the fractional module S-1M over the fractional ring S-1R had invariant factors whenever the multiplicative subset S of R was invertible in R/AnnR(M) being the annihilator of M in R. 探讨了交换环R上具有不变因子的模M之判别问题,证明了只要R的乘法子集S在R/AnnR(M)中可逆,则M为具有不变因子的R-模当且仅当分式模S-1M为分式环S-1R上的具有不变因子的模. 短句来源 Viewing modules M S -1 R over a fractional ring S -1 R of a ring R as modules M R over R ,It is proved that some model theoretic properties of modules,such as purity,pure embedding,elementary equivalence,elementary embedding,are preserved. 将环R的分式环S－1R上的模MS－1R“限制”到R上时，模理论的纯性、纯入射性、初等等价、初等嵌入等模型论性质都是保持的。 短句来源 The fractional ring(module)and the interrelated localization method are the important tools for commutative algebra. 分式环和分式模以及与之相关的局部化方法是交换代数中一个重要工具. 短句来源 These results will take an important part in studying fractional ring (module),localization method and projective geometry. 这些结果无疑对更进一步研究分式环(模)及局部化方法,特别是投射几何代数的研究大有裨益. 短句来源 Our main result in this paper is thatnon-commutative non-associative fractional ring with right inverse property is alternative. 主要结果是对于具有右逆性质的非交换非结合分式环S~(-1)R,必是交错的。 短句来源
 分式环的
 THE ASSOCIATOR THEORY OF NON—COMMUTATIVE NON—ASSOCIATIVE FRACTIONAL RING 非交换非结合分式环的结合子理论 短句来源 ALTERNATIVE OF NON—COMMUTATIVE NON—ASSOCIATIVE FRACTIONAL RING 非交换非结合分式环的交错性 短句来源 This paper studies the problems on semiprime PI ring by utilizing the properties of subdirectly irreducible ring and fractional ring and proves an important commutativity theorem on semiprime PI ring . 本文利用亚直不可约环和分式环的性质 ,研究了任意半质 PI-环的交换性问题 ,证明了半质 PI-环的交换性定理 . 短句来源

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 fractional ring
 Given a commutative ring A equipped with a preordering A+ (in the most general sense, see below), we look for a fractional ring extension (= "ring of quotients" in the sense of Lambek et al.
 The fractional ring(module)and the interrelated localization method are the important tools for commutative algebra.We have had a lot of results for themselves.In this paper,we study the associator theory of fractional ring of non-commutative non-associative rings.These results will take an important part in studying fractional ring (module),localization method and projective geometry. 分式环和分式模以及与之相关的局部化方法是交换代数中一个重要工具.而对分式环和分式模本身的研究也有许多结果.不过这些均假定基础环是可交换可结合的,而对基础环不满足交换性甚至不满足结合性却结果极少.本文在这样的假设下,研究了非交换非结合环 R对于其乘法集 S 的分式环 S~1R 的结合子理论,并得到了一系列的结果.这些结果无疑对更进一步研究分式环(模)及局部化方法,特别是投射几何代数的研究大有裨益. We studied the associator and commutator of non-commutative non-associative frac-tional ring in Paper One. This paper is its continuation. Our main result in this paper is thatnon-commutative non-associative fractional ring with right inverse property is alternative. 我们在文[1]中研究了非交换非结合分式环的结合子与换位子理论,本文是[1]的继续。主要结果是对于具有右逆性质的非交换非结合分式环S~(-1)R,必是交错的。 Viewing modules M S -1 R over a fractional ring S -1 R of a ring R as modules M R over R ,It is proved that some model theoretic properties of modules,such as purity,pure embedding,elementary equivalence,elementary embedding,are preserved.The relations of such properties between M R and ( S -1 M) S -1 R are also considered. 将环Ｒ的分式环Ｓ－１Ｒ上的模ＭＳ－１Ｒ“限制”到Ｒ上时，模理论的纯性、纯入射性、初等等价、初等嵌入等模型论性质都是保持的。还讨论了（Ｓ－１Ｍ）Ｓ－１Ｒ与ＭＲ之间模型论性质的保持性 << 更多相关文摘
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