tensor product for a commutative Ring

1. Definition

Let 20230801-tensor_product_6130b692b4d58a44d70e323b9432701598ebebee.svg be a commutative ring, 20230801-tensor_product_2273b15653e62f647e7bff48b42dac4fad211430.svg 20230801-tensor_product_d9fed023a9d07263c522f5c4dbb780117ad7ad02.svg-modules. Then a tensor product 20230801-tensor_product_1e75ef27324f0d8a63055b223d2a01cae2dc9254.svg is a 20230801-tensor_product_d9fed023a9d07263c522f5c4dbb780117ad7ad02.svg-module 20230801-tensor_product_85b0b5f834f1d715f4a19258070f3afca7a3cbe5.svg with a homomorphism 20230801-tensor_product_f0558bdee8321cb1ce34f49172c927e9ac61fe5e.svg satisfying the following universal property:

For any module 20230801-tensor_product_cd0ff9796d5d44181802247ecadcd48ba7fe30fc.svg and bilinear map 20230801-tensor_product_3f4df379e61d057fb771d6608bae023667a413bf.svg there exists a unique module-homomorphism 20230801-tensor_product_c69e63940e9aa0f860165a7f913b244dff27cd78.svg such that diagramm commutes

20230801-tensor_product_36b463ff4b3dd2d622e2a4604fde474404be0664.svg

2. See

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 15:34