Some additive combinatorics problems in matrix rings
نویسندگان
چکیده
منابع مشابه
Some Additive Combinatorics Problems in Matrix Rings
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers. 2000 Mathematics Subject Classification. 11C20, 11D79, 11T23
متن کاملSome Problems in Combinatorics
Let In = {1, 2, . . . , n} and x : In 7→ R be a map such that ∑ i∈In x(i) ≥ 0. (For any i, its image is denoted by x(i).) Let F = {J ⊂ In : |J | = k, and ∑ j∈J x(j) ≥ 0}. In [25] Manickam and Singhi have conjectured that |F| ≥ ( n−1 k−1 ) whenever n ≥ 4k and showed that the conclusion of the conjecture holds when k divides n. For any two integers r and ` let [r]` denote the smallest positive in...
متن کامل5 Some additive galois cohomology rings
Let p ≥ 3 be a prime. We consider the cyclotomic extension Z (p) [ζ p 2 ] | Z (p) , with galois group G = (Z/p 2) *. Since this extension is wildly ramified, the Z (p) G-module Z (p) [ζ p 2 ] is not projective. We calculate its cohomology ring H * (G, Z (p) [ζ p 2 ]; Z (p)), carrying the cup product induced by the ring structure of Z (p) [ζ p 2 ]. Formulated in a somewhat greater generality, ou...
متن کاملSome cyclotomic additive Galois cohomology rings
Let p ≥ 3 be a prime. We consider the cyclotomic extension Z(p)[ζp2] of Z(p), with Galois group G := (Z/p2)∗. Since this extension is wildly ramified, Z(p)[ζp2] is not projective as a module over the group ring Z(p)G (Speiser). Extending this module structure, we can regard Z(p)[ζp2 ] as a module over the twisted group ring Z(p)[ζp2] ≀G; as such, it remains faithful and non projective. We calcu...
متن کاملOn Identities with Additive Mappings in Rings
begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2010
ISSN: 1139-1138,1988-2807
DOI: 10.1007/s13163-010-0029-4