整数环 meaning in English

integral ring
ring of integers

On necessary and sufficient condition of invertible matrix in integral ring
整数环上矩阵可逆的充要条件
Positive definite even unimodular lattices over real quadratic integer rings
实二次整数环上的正定偶幺模格
On the classification of positive definite unimodular lattices over the rings of real quadratic integers
实二次代数整数环上的正定幺模格的分类