A note on involution rings
TL;DR: In this article, the structure of certain involution rings in which the norms are multiplicatively generated by nilpotents is also determined, and the classifications of subdirectly irreducible involution ring via some properties of trace elements are given.
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Abstract: Classifications of subdirectly irreducible involution rings via some properties of trace elements are given. As an application, von Neumann regular involution rings with central idempotent norm elements are described. The structure of certain involution rings in which the norms are multiplicatively generated by nilpotents is also determined. 2000 Mathematics Subject Classification: 16N60, 16W10
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Citations
Reversible Rings with Involutions and Some Minimalities
Wafaa M. Fakieh,S. K. Nauman +1 more
TL;DR: It is proved here that the polynomial rings of ∗-reversible rings may not be ∗ -reversible, and a criterion for rings which cannot adhere to any involution is developed.
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On rings with involution and inner rings
01 Jan 2024
TL;DR: This article extends results from matrix rings to rings with involution, introducing concepts for Hermitian, skew-Hermitian, and normal elements, norms, orthogonality, and order, and defining inner rings with properties examined.
1
References
Prime ideals in rings with involution
TL;DR: In this paper, it was shown that if R is a *-prime ring which is not a prime ring, then R is essentially a direct product of two prime rings, and if P is a prime ideal of R, then X is minimal among prime ideals of R containing P, P = X ∩ X* and either: (1) P is essential in X and X is essential on R; or (2) for any relative complement C of P in X, then C* is a relative complement of X in R.
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Rings with involution and chain conditions
K.I. Bec̆dar,R. Wiegandt +1 more
TL;DR: The structure of rings with d.c. on ∗-biideals is investigated in this paper, where a polynomial ring A [x ] over an associative ring A has a.c., and if A is finite and semiprime, then its Baer radical is finitely generated as an abelian group.
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