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中文摘要：
讨论了环由子集生成的子环、子环的和与积的结构，子环的积对和的分配关系，证明了结合环类是完备代数类及可积代数类，从而是完备代数正规类及可积代数正规类．
英文摘要：
The structures of the subring generated by a subset of a ring, the structures of sum and product of subrings, the distribution product over the sum of subrings are discovered, it is showen that the class of associative rings is a class of complete algebras and a class of product algebras, so it is a normal class of complete algebras and a normal class of product algebras.
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