منابع مشابه
Rings as Groups with Operators
(11) KM s 0 (mod 2*--9). Conversely (11) implies (9). Since (9) holds for the modulus 2-9ikf, it follows similarly that (11) holds for the modulus 2~-9 with ikf = 2ikfi. Hence (11) will be true for the given modulus if M = 2~M\. This supplies a proof by induction that (8) is a universal form for every w ^ 4 . If, in addition,* ikf is divisible by every prime p where 3<p^n, we satisfy the necess...
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Jacobson's generalization [5, Theorem 8] of Wedderburn's theorem [8] states that an algebraic division algebra over a finite field is commutative. These algebras have the property that some power2 of each element lies in the center. Kaplansky observed in [7] that any division ring, or, more generally, any semisimple ring, in which some power of each element lies in the center is commutative. Ka...
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Let G be a connected, simple Lie group of rank n defined over the complex numbers. To a parabolic subgroup P in G of semisimple rank r, one can associate n−r positive integers coming from the theory of hyperplane arrangements (see P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), 167-189; Coxeter arrangements, in Proc. of Symposia in Pur...
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in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.
متن کاملCommutative Subdirectly Irreducible Radical Rings
A ring R is radical if there is a ring S (with unit) such that R = J (S) (the Jacobson radical). We study the commutative subdirectly irreducible radical rings and show that such a ring is noetherian if and only if is finite. We present a reflection of the commutative radical rings into the category of the commutative rings and derive a lot of examples of the subdirectly irreducible radical rin...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8996