求和的伸缩、乘法和有理扩张
Telescopic, Multiplicative, and Rational Extensions of Summations
摘要：
求和是从${\rm R}[[σ]]$的子模到${\rm R}$或另一个环的移位不变${\rm R}$ -模同态。[11]形式化了一种通过伸缩将求和扩展到更大域的方法。在本文中，我们重新伸缩，我们研究乘法封闭的求和（如通常的总和收敛级数），本身不是乘法封闭的，我们研究合理的扩展作为一个推广的伸缩。
英文摘要：
A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[σ]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we revisit telescoping, we study multiplicative closures of summations (such as the usual summation on convergent series) that are not themselves multiplicatively closed, and we study rational extensions as a generalization of telescoping.
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