Jordan isomorphisms and additive rank preserving maps on symmetric matrices over PID

DOI10.1016/j.laa.2006.04.022zbMath1172.17022OpenAlexW2054522183MaRDI QIDQ865396

De-Qiong Li, Tao Ban, Kang Zhao, Li-Ping Huang

Publication date: 14 February 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2006.04.022

zbMATH Keywords

symmetric matrixJordan isomorphismsadditive rank preserving mapsprincipal ideal domain (PID)

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Jordan structures associated with other structures (17C50)

Related Items (2)

Jordan derivation of certain Jordan matrix algebras ⋮ Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices

Cites Work

• Characterization of Jordan homomorphism on \(M_ n\) using preserving properties
• Additive Jordan isomorphisms of nest algebras on normed spaces
• Jordan isomorphisms of triangular matrix algebras over a connected commutative ring
• Jordan elementary maps on rings.
• Additivity of Jordan maps on standard operator algebras
• Additive rank-one preserving surjections on symmetric matrix spaces
• Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings
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