Zero divisors with small supports in group algebras of torsion-free groups over a fieldRabindranath ChakrabortySourav Koner
References in periodicals archive? An element a [member of] h(R) is called azerodivisoron M if am = 0 for some m [member of] h(M). Properties of [phi]-Primal Graded Ideals More results ► Full browser? Complete English Grammar Rules ...
way. The equalitya· 0 = 0 ·a= 0 is always satisfied in a ring. If the product of two elements in a ring is equal to zero, it does not necessarily follow that one of the factors is equal to zero; ifab= 0 anda≠ 0 andb≠ 0, then the elementsaandbare called divisors of ...
We consider the following problem: If KG is the group ring of a torsion free group over a field K, show that KG has no divisors of zero. At characteristic zero, major progress was made by Brown [ 2 ], who solved the problem for G abelian-by-finite, and then by Farkas and Snider ...
8.There need be no patsy, because the economy is not a zero-sum game.这里不应该有替罪羊,因为经济并非零和游戏。 9.ZERO ENERGY FERMION IN TOPOLOGICAL NONTRIVIAL SPHERICAL SYMMETRICAL FIELD ON MINKOWSKI SPACE闵空间拓扑非平庸球对称场中零能费米子 10.Geometry of Submanifolds in Riemannian Spin Manifo...
The zero-divisor graph Γ(R) of a ring R has vertices the zero-divisors in R (the non-zero elements a for which there exists b≠0 such that ab=0), with an edge {a,b} whenever ab=0. The zero-divisor graphs have been extensively studied in the past [1], [3], [4], [5],...
Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element a in R[G] as the minimal non-negative integer k for which there are ring element...
Let $A$ be a Noetherian local ring with residue field $\kappa$. Let $a, b \in A$. Let $M$ be a finite $A$-module of dimension $1$ such that $a, b$ are nonzero-divisors on $M$. such that $a, b$ are nonzerodivisors on $M$. We define the {\it symbol associated to ...
A ring which has no zero divisors except {eq}0 {/eq} itself, such as {eq}\mathbb{Z} {/eq}, is called an integral domain. A ring whose nonzero elements are all units, such as {eq}\mathbb{Q} {/eq}, is called a field. ...
Throughout this paper, we assume that R is a finite commutative non-local ring with identity, Z(R) its set of zero-divisors and R× its group of units, Fq the field with q elements, and R∗=R−{0}. Now let us summarize notations, concepts and results related to the planarity ...