Mathematics, 22.07.2021 06:20, pcruznoel6624

Giả sử X là vành tùy ý, Z là vành các số nguyên. Xét tập E = X × Z, trên E ta định nghĩa 2 phép toán như sau:
(x1, n1)+(x2, n2) = (x1+x2, n1+n2), (x1, n1)∗(x2, n2) = (x1x2+n1x2+n2x1, n1n2)
Chứng minh rằng:
a. E là vành có đơn vị.
b. Hàm f : X → E xác định bởi f(x) = (x, 0) là đơn cấu (vành).

Answers: 1

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Giả sử X là vành tùy ý, Z là vành các số nguyên. Xét tập E = X × Z, trên E ta định nghĩa 2 phép toá...