Additivity of maps preserving triple product on *-ring | Zendy

Ali Taghavi | Zendy; Mehran Razeghi | Zendy; Mojtaba Nouri | Zendy; Vahid Darvish | Zendy; Changjing Li | Zendy

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Additivity of maps preserving triple product on *-ring

Author(s) -

Ali Taghavi,

Mehran Razeghi,

Mojtaba Nouri,

Vahid Darvish,

Changjing Li

Publication year - 2020

Publication title -

boletim da sociedade paranaense de matemática

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.347

H-Index - 15

eISSN - 2175-1188

pISSN - 0037-8712

DOI - 10.5269/bspm.40370

Subject(s) - bijection , projection (relational algebra) , additive function , prime (order theory) , mathematics , combinatorics , ring (chemistry) , product (mathematics) , geometry , mathematical analysis , algorithm , chemistry , organic chemistry

Let A and B be two prime ∗-rings. Let Φ : A → B be a bijective and satisfies Φ(A •λ P •λ P ) = Φ(A) •λ Φ(P ) •λ Φ(P ), for all A ∈ A and P ∈ {I, P1, I − P1} where P1 is a projection in A. The operation •λ between two arbitrary elements S and T in A is defined as S •λ T = ST + λTS ∗ for λ ∈ {−1, 1}. Then, if Φ(I) is projection, we show that Φ is additive.

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