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<p>The author continues to study lattice isomorphisms of finite matrix rings. In this paper, it is proved that if <i>R = M</i><sub><i>n</i></sub>(<i>K</i>)<i>, </i><i>n</i> ≥ 3<i>, </i><i>K</i> is a finite ring with identity, and <i>φ</i> is a lattice isomorphism of a ring <i>R</i> onto a ring <i>R</i><sup><i>φ</i></sup>, then the following statements hold: (1) <i>R</i><sup><i>φ</i></sup> ≅ <i>R</i> and (2) if the additive group of the ring <i>R</i> is primary, then the lattice isomorphism <i>φ</i> is induced by a ring isomorphism or anti-isomorphism of <i>R</i> onto <i>R</i><sup><i>φ</i></sup><i>.</i></p>

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Lattice Definability of Finite Matrix Rings

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • S. S. Korobkov

摘要

The author continues to study lattice isomorphisms of finite matrix rings. In this paper, it is proved that if R = Mn(K), n ≥ 3, K is a finite ring with identity, and φ is a lattice isomorphism of a ring R onto a ring Rφ, then the following statements hold: (1) Rφ ≅ R and (2) if the additive group of the ring R is primary, then the lattice isomorphism φ is induced by a ring isomorphism or anti-isomorphism of R onto Rφ.