A squarefree module over a polynomial ring S = k[x1, . . . , xn] is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals more systematically. The category Sq of squarefree modules is equivalent to the category of finitely generated left Λ-modules, where Λ is the incidence algebra of the Boolean lattice 2. The derived category D(S...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

A linear interpolation scheme is termed ‘ideal’ when its errors form a polynomial ideal. The paper surveys basic facts about ideal interpolation and raises some questions. Ideal interpolation is, by definition, given by a linear projector on the space Π of polynomials whose kernel is a polynomial ideal. It is therefore also any linear map, as used in algebra, that associates a polynomial with i...

The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$,  we mean an ideal $I$ of $R$ such that $Ineq R$.  We say that a proper ideal $I$ of a ring $R$ is a  maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...

Abstract Can one tell if an ideal is radical just by looking at the degrees of generators? In general, this hopeless. However, there are special collections in multigraded polynomial rings, with property that any generated elements those radical. We call such a collection support. paper, we give combinatorial characterization supports. Our terms properties cycles associated labelled graph. also...

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...

Self-Discrepancy Theory (SDT) proposes that ideal-self discrepancies predict dejection/depression and ought-self discrepancies predict agitation/anxiety, but individual differences research has rarely found clear support for this pattern. After considering methodological and statistical reasons for these mixed findings, the present research tested SDT’s predictions using a multivariate structur...

The design of linear image filters based on properties of human visual perception has been shown to require the minimization of criterion functions in both the spatial and frequency domains. We extend this approach to continuous filters of infinite support. For lowpass filters, this leads to the concept of an ideal lowpass image filter that provides a response that is superior perceptually to t...