Some conditions on commutative semiprime rings
نویسندگان
چکیده
منابع مشابه
T -rough Semiprime Ideals on Commutative Rings
Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T -rough semiprime ideal, T -rough fuzzy semiprime ideal and T -rough quotient ideal in a commutative rin...
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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.
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This article explores several extensions of the Prüfer domain notion to rings with zero divisors. These extensions include semihereditary rings, rings with weak global dimension less than or equal to 1, arithmetical rings, Gaussian rings, locally Prüfer rings, strongly Prüfer rings, and Prüfer rings. The renewed interest in these properties, due to their connection to Kaplansky’s Conjecture, ha...
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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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1969
ISSN: 0021-8693
DOI: 10.1016/0021-8693(69)90084-2