Structure of semiprime {\rm P}.{\rm I}. rings
نویسندگان
چکیده
منابع مشابه
Centralizers on semiprime rings
The main result: Let R be a 2-torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T (xyx) = xT (y)x holds for all x, y ∈ R. In this case T is a centralizer.
متن کاملFuzzy semiprime ideals in -rings
In this paper, T. K. Dutta`s and S. K. Sardar`s semiprime ideal of -rings as a fuzzy semiprime ideal of a -rings via its operator rings was defined. Some characterizations of fuzzy semiprime ideal of -rings was obtained. That is; a characterization prove of a fuzzy semiprime ideal, the relationship between fuzzy semiprime ideal and fuzzy prime ideal was obtained. If is fuzzy semiprime ideal of ...
متن کاملCentralizers on prime and semiprime rings
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let R be a noncommutative prime ring of characteristic different from two and let S and T be left centralizers on R. Suppose that [S(x), T (x)]S(x) + S(x)[S(x), T (x)] = 0 is fulfilled for all x ∈ R. If S 6= 0 (T 6= 0) then there exists λ from the extende...
متن کاملOn Θ-centralizers of Semiprime Rings (ii)
The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0320049-0