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1.
D. S. Bazhenov 《Moscow University Mathematics Bulletin》2017,72(2):70-72
Prime Goldie rings graded by a group are studied. It is proved that there exists a completely gr-reducible graded ring of fractions in the case of a grading group with a finite commutator subgroup (which enhances the results of Goodearl–Stafford obtained for Abelian groups). An example where such ring does not exist is constructed (a counterexample for a semi-prime ring was already known). 相似文献
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We investigate in this paper rings whose proper ideals are 2-primal. We concentrate on the connections between this condition and related concepts to this condition, and several kinds of π-regularities of rings which satisfy this condition. Moreover, we add counterexamples to the situations that occur naturally in the process of this note. 相似文献
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Differential identities of prime rings 总被引:10,自引:0,他引:10
V. K. Kharchenko 《Algebra and Logic》1978,17(2):155-168
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Dinh Van Huynh S. K. Jain S. R. Ló pez-Permouth 《Proceedings of the American Mathematical Society》2000,128(11):3153-3157
It is shown that: (a) If is a prime right Goldie right CS ring with right uniform dimension at least 2, then is left Goldie, left CS; (b) A semiprime ring is right Goldie left CS iff is left Goldie, right CS.
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Let f be a function from a finite field with a prime number p of elements, to . In this article we consider those functions f(X) for which there is a positive integer with the property that f(X)i, when considered as an element of , has degree at most p−2−n+i, for all i=1,…,n. We prove that every line is incident with at most t−1 points of the graph of f, or at least n+4−t points, where t is a positive integer satisfying n>(p−1)/t+t−3 if n is even and n>(p−3)/t+t−2 if n is odd. With the additional hypothesis that there are t−1 lines that are incident with at least t points of the graph of f, we prove that the graph of f is contained in these t−1 lines. We conjecture that the graph of f is contained in an algebraic curve of degree t−1 and prove the conjecture for t=2 and t=3. These results apply to functions that determine less than directions. In particular, the proof of the conjecture for t=2 and t=3 gives new proofs of the result of Lovász and Schrijver [L. Lovász, A. Schrijver, Remarks on a theorem of Rédei, Studia Sci. Math. Hungar. 16 (1981) 449–454] and the result in [A. Gács, On a generalization of Rédei’s theorem, Combinatorica 23 (2003) 585–598] respectively, which classify all functions which determine at most 2(p−1)/3 directions. 相似文献
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Groups whose subnormal subgroups have bounded defect 总被引:1,自引:0,他引:1
Trevor Hawkes 《Archiv der Mathematik》1984,43(4):289-294
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The main theorem states that if f(x
1, x
2, x
3) is an indefinite anisotropic integral quadratic form with determinant d(f), and t a non-zero integer such that d(f)t is square-free, then as long as there is one integer solution to f(x
1, x
2, x
3) = t there are infinitely many such solutions for which the product x
1
x
2
x
3 has at most 26 prime factors. The proof relies on the affine linear sieve and in particular automorphic spectral methods
to obtain a sharp level of distribution in the associated counting problem. The 26 comes from applying the sharpest known
bounds towards Selberg’s eigenvalue conjecture. Assuming the latter the number 26 may be reduced to 22. 相似文献
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Let R[x; δ] be a differential polynomial ring over a prime Goldie ring R in an indeterminate x, where δ is a derivation of R. In this paper, we describe explicitly the group of δ-stable v-R-ideals and using this results, we show that R[x; δ] is a generalized Asano prime ring if and only if R is a δ-generalized Asano prime ring. 相似文献
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James McTigue 《Linear algebra and its applications》2011,435(9):2259-2271
A partial matrix over a field F is a matrix whose entries are either elements of F or independent indeterminates. A completion of such a partial matrix is obtained by specifying values from F for the indeterminates. We determine the maximum possible number of indeterminates in a partial m×n matrix whose completions all have rank at least equal to a particular k, and we fully describe those examples in which this maximum is attained. Our main theoretical tool, which is developed in Section 2, is a duality relationship between affine spaces of matrices in which ranks are bounded below and affine spaces of matrices in which the (left or right) nullspaces of elements possess a certain covering property. 相似文献
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It follows from classical results of Neumann and Macdonald that a group G has finite commuator subgroup if and only if either the normalizers of cyclic subgroups of G have boundedly finite indices or cyclic subgroups of G have bounded indices in their normal closures. In this paper, groups with a similar condition are considered, when normality
is replaced by permutability.
相似文献
15.
Hung P. Tong-Viet 《Israel Journal of Mathematics》2014,202(1):295-319
Let G be a finite group and let p be a prime. In this paper, we classify all finite quasisimple groups in which the degrees of all irreducible p-Brauer characters are prime powers. As an application, for a fixed odd prime p, we classify all finite nonsolvable groups with the above-mentioned property and having no nontrivial normal p-subgroups. Furthermore, for an arbitrary prime p, a complete classification of finite groups in which the degrees of all nonlinear irreducible p-Brauer characters are primes is also obtained. 相似文献
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Francesc Planas-Vilanova 《Journal of Pure and Applied Algebra》2021,225(2):106494
Let R be a Noetherian ring. We prove that R has global dimension at most two if, and only if, every prime ideal of R is of linear type. Similarly, we show that R has global dimension at most three if, and only if, every prime ideal of R is syzygetic. As a consequence, we derive a characterization of these rings using the André-Quillen homology. 相似文献
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Weimin Xue 《代数通讯》2013,41(5):2633-2638
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Let &PHgr; n (z) = ∑ ϕ (n) m=0 a (m, n) z m be the n th cyclonomic polynomial and set A(n) = max 0≤m≤ϕ(n) |a=(m, n)|. In previous papers the author has shown that for almost all integers A(n)≤ n &PHgr;(n) ; whenever lim n→∞ &PHgr;(n) = ∞ . In this paper we show that for most integers n with at least C log log n prime factors ( C > 2/log 2) this inequality is wrong. 相似文献