多项式和幂级数 (I)

Like Like Love Haha Wow Sad Angry 今天我们讨论多项式 交换环上 Nilpotents and units are closely related. In a commutative unital ring , if nilpotent, unit, then is again a unit. If is a unit for every , then , the Jacobson radical, approximately nilpotent. Read by: 73 Like Like Love Haha Wow S……

《交换代数》习题研讨 (I)

Like Like Love Haha Wow Sad Angry Units, nilpotents, and idempotents lift from to .Proof: Units and nilpotents are obvious. In fact they lift to any of their representatives. For idempotents, if , then , so for sufficiently large . And , so lifts to a unit . Moreover, its inverse……

一个简单的组合问题及相关的思考

Like Like Love Haha Wow Sad Angry Problem: If the decimal expansion of contains all digits (), then the number of length strings (shorted as -strings) is greater than . If you’ve established the simple lemma, the solution is instant. Otherwise very impossible. Lemma: The nu……

生成函数和形式幂级数

Like Like Love Haha Wow Sad Angry 今天我们讨论生成函数 Problem 1: Give a finite set of positive integers . Let be the collection of sequences , such that , and each . Let for and , and . Find out what is explicitly. Solution: It is not hard to note the recursive relation for , if we set fo……