Jordan* multiplicative maps on prime * rings
Zhang Fang-jua
Abstract
Zhang Fang-jua
Abstract
Let A be a unital prime * ring containing a nontrivial projection P.Using methods of standard argument,it is shown that Jordan* multiplicable bijective maps and Jordan* triple multiplicable bijective maps on A are *-isomorphisms or *-anti-isomorphisms.It is shown that ф:A→A is a bijective map and satisfies ф(AB*+ B*A) = ф(A) ф(B)*+ ф(B)*ф(A) for every pair A,B∈A if and only if ф is a *-ring isomorphism,or a *-ring anti-isomorphism;ф is a bijective map and satisfies ф(AB*A) = ф(A) ф(B)*ф(A) for every pair A,B∈A if and only if ф is a *-isomorphism,or a conjugate *-isomorphism,or a *-anti-isomorphism,or a conjugate *-anti-isomorphism.
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Let A be a unital prime * ring containing a nontrivial projection P.Using methods of standard argument,it is shown that Jordan* multiplicable bijective maps and Jordan* triple multiplicable bijective maps on A are *-isomorphisms or *-anti-isomorphisms.It is shown that ф:A→A is a bijective map and satisfies ф(AB*+ B*A) = ф(A) ф(B)*+ ф(B)*ф(A) for every pair A,B∈A if and only if ф is a *-ring isomorphism,or a *-ring anti-isomorphism;ф is a bijective map and satisfies ф(AB*A) = ф(A) ф(B)*ф(A) for every pair A,B∈A if and only if ф is a *-isomorphism,or a conjugate *-isomorphism,or a *-anti-isomorphism,or a conjugate *-anti-isomorphism.
Key concepts: Bijection, Isomorphism (crystallography), Mathematics, Multiplicative function, Ring (chemistry), Combinatorics, Prime (order theory), Pure mathematics