Abstract Given a subdirectly irreducible ∗-regular ring R, we show that R is a homomorphic image of a regular ∗-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular. For any subdirect product of artinian ∗-regular rings we construct a unit-regular and ∗-clean extension within its variety.

中文翻译：

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∗-规则环的种类

摘要 给定一个次直接不可约 ∗ 正则环 R，我们证明 R 是（简单）eRe 的超积的正则 ∗ 子环的同态映象，e 在 R 的极小理想中；此外，如果所有 eRe 都是单位正则的，则 R（带单位）是直接有限的。对于artinian ∗-regular 环的任何子直积，我们在其种类中构造了一个unit-regular 和∗-clean 扩展。