منابع مشابه
When is the ring of real measurable functions a hereditary ring?
Let $M(X, mathcal{A}, mu)$ be the ring of real-valued measurable functions on a measure space $(X, mathcal{A}, mu)$. In this paper, we characterize the maximal ideals in the rings of real measurable functions and as a consequence, we determine when $M(X, mathcal{A}, mu)$ is a hereditary ring.
متن کاملChromophores in Molecular Nanorings: When Is a Ring a Ring?
The topology of a conjugated molecule plays a significant role in controlling both the electronic properties and the conformational manifold that the molecule may explore. Fully π-conjugated molecular nanorings are of particular interest, as their lowest electronic transition may be strongly suppressed as a result of symmetry constraints. In contrast, the simple Kasha model predicts an enhancem...
متن کاملThe annihilator-inclusion Ideal graph of a commutative ring
Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...
متن کاملThe sum-annihilating essential ideal graph of a commutative ring
Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...
متن کاملStudy on the new graph constructed by a commutative ring
Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation b...
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: International Journal of Mathematics and Mathematical Sciences
سال: 1993
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171293000766