Multiplier ideals are very important in higher dimensional geometry to study the singularities of ideal sheaves. It reflects the singularities of the ideal sheaves and provides strong vanishing theorem called the Kawamata-Viehweg-Nadel vanishing theorem (see [3]). However, the multiplier ideals are defined via a log resolution of the ideal sheaf and divisors on the resolved space, and it is dif...

We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with fuller generality, and at the same time, obtain new results. Past investigations on the resolutions of edge ideals usually reduced the problem to computing the di...

Culture specifies standards for women’s and men’s body appearance and display. In Western cultures, these standards are both concentrated and ubiquitous in the media, represented as gendered body ideals for citizens to aspire toward. Because gendered body ideals are revered, individuals try to construct and portray their body consistently with these ideals. Furthermore, because gendered body id...

A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T ∧-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T ∧-fuzzy (implicative) ideal are provided. Some...

In the paper, we give the concept of ¬-ideals dual to that of ¬-filters by using the operation ~ in SBL¬-algebras, and also show some characterizations of ¬-ideals. The relationships between ¬-ideals and ¬filter are investigated by the notion of the set of complement elements. It is obtained that for a ¬-proper ideal I of a SBL¬-algebra L, the set I ∪N(I) is the least SBL¬-subalgebra of L conta...

Using the idea of prime and semiprime bi-ideals of rings, the concept of prime and semiprime generalized bi-ideals of rings is introduced, which is an extension of the concept of prime and semiprime bi-ideals of rings and some interesting characterizations of prime and semiprime generalized bi-ideals are obtained. Also, we give the relationship between the Baer radical and prime and semiprime g...