Rings with zero intersection property on annihilators: Zip rings
نویسندگان
چکیده
منابع مشابه
On cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
متن کاملon cycles in intersection graphs of rings
let $r$ be a commutative ring with non-zero identity. we describe all $c_3$- and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. also, we shall describe all complete, regular and $n$-claw-free intersection graphs. finally, we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...
متن کاملOn Polynomial Rings with a Goldbach Property
David Hayes observed in 1965 that when R = Z, every element of R[T ] of degree n ≥ 1 is a sum of two irreducibles in R[T ] of degree n. We show that this result continues to hold for any Noetherian domain R with infinitely many maximal ideals. It appears that David Hayes [5] was the first to observe the following polynomial analogue of the celebrated Goldbach conjecture: If R = Z, then (?) ever...
متن کاملQuantum intersection rings
* Laboratoire de la Direction des Sciences de laMatì ere du Commissariatà l'Energie Atomique.
متن کاملOn quasi-zero divisor graphs of non-commutative rings
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 1989
ISSN: 0214-1493
DOI: 10.5565/publmat_33289_09