Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding code ideals are related by elimination...

We propose a technique for obtaining solutions to ordinary differential equations. A system of differential equations sometimes has multiple solutions with distinct features. Prime ideal decomposition can be used for extracting the desired solution from these solutions. Solutions to algebraic equations contain many parameters, and in such a case, prime ideal decomposition is less tractable. As ...

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...

Let [Formula: see text] be a commutative ring with unity. The prime ideal sum graph of the is simple undirected whose vertex set nonzero proper ideals and two distinct vertices are adjacent if only text]. In this paper, we characterize all finite non-local rings genus

In this paper, T. K. Dutta`s and S. K. Sardar`s semiprime ideal of -rings as a fuzzy semiprime ideal of a -rings via its operator rings was defined. Some characterizations of fuzzy semiprime ideal of -rings was obtained. That is; a characterization prove of a fuzzy semiprime ideal, the relationship between fuzzy semiprime ideal and fuzzy prime ideal was obtained. If is fuzzy semiprime ideal of ...