منابع مشابه
Suslin's algorithms for reduction of unimodular rows
A well-known lemma of Suslin says that for a commutative ring A if (v1(X), . . . , vn(X)) ∈ (A[X])n is unimodular where v1 is monic and n ≥ 3, then there exist γ1, . . . , γ` ∈ En−1(A[X]) such that the ideal generated by Res(v1, e1.γ1 (v2, . . . , vn)), . . . , Res(v1, e1.γ` (v2, . . . , vn)) equals A. This lemma played a central role in the resolution of Serre’s conjecture. In case A contains ...
متن کاملCommutative Monoid Rings as Hilbert Rings
Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...
متن کاملOn zero divisor graph of unique product monoid rings over Noetherian reversible ring
Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $Gamma(R)$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring o...
متن کاملOn quasi-Armendariz skew monoid rings
Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...
متن کاملSome remarks on orbit sets of unimodular rows
Let A be a d -dimensional smooth algebra over a perfect field of characteristic not 2. Let UmnC1.A/=EnC1.A/ be the set of unimodular rows of length n C 1 up to elementary transformations. If n .d C 2/=2, it carries a natural structure of group as discovered by van der Kallen. If n D d 3, we show that this group is isomorphic to a cohomology group H .A;G/. This extends a theorem of Morel, who sh...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.08.011