Minimal ideal

About: Minimal ideal is a research topic. Over the lifetime, 740 publications have been published within this topic receiving 7755 citations.

A generalization of tight closure and multiplier ideals

Abstract: We introduce a new variant of tight closure associated to any fixed ideal a, which we call α-tight closure, and study various properties thereof In our theory, the annihilator ideal r(a) of all α-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role We prove the correspondence of the ideal τ(a) and the multiplier ideal associated to a (or, the adjoint of a in Lipman's sense) in normal Q-Gorenstein rings reduced from characteristic zero to characteristic p >> 0 Also, in fixed prime characteristic, we establish some properties of r(a) similar to those of multiplier ideals (eg, a Briancon-Skoda-type theorem, subadditivity, etc) with considerably simple proofs, and study the relationship between the ideal τ(α) and the F-rationality of Rees algebras

Jordan homomorphisms of rings

Abstract: The primary aim of this paper is to study mappings J of rings that are additive and that satisfy the conditions $$ {\left( {{a^2}} \right)^J} = {\left( {{a^J}} \right)^2},\;{\left( {aba} \right)^J} = {a^J}{b^J}{a^J} $$ (1) Such mappings will be called Jordan homomorphisms. If the additive groups admit the operator 1/2 in the sense that 2x = a has a unique solution (1/2)a for every a, then conditions (1) are equivalent to the simpler condition $$ {\left( {ab} \right)^J} + {\left( {ba} \right)^J} = {a^J}{b^J} + {b^J}{a^J} $$ (2) Mappings satisfying (2) were first considered by Ancochea [1], [2](1). The modification to (1) is essentially due to Kaplansky [13]. Its purpose is to obviate the necessity of imposing any restriction on the additive groups of the rings under consideration.

Rees algebras of edge ideals

Abstract: Let G be a graph and let I be its edge ideal. We express the presentation ideal of R(I), the Rees algebra of I, in terms of the syzygies of I and the presentation ideal of the special fiber of R(I). A description of the elementary integral vectors of the kernel of the incidence matrix of G is given and then used to study the special fiber of R(I) via Grobner bases.

(ε, ε ν q)-fuzzy subnear-rings and ideals

Abstract: Our aim in this paper is to introduce and study the new sort of fuzzy subnear-ring (ideal and prime ideal) of a near-ring called (?, ? ?q)-fuzzy subnear-ring (ideal and prime ideal). These fuzzy subnear-rings (ideals) are characterized by their level ideals. Finally, we give a generalization of (?, ? ?q)-fuzzy subnear-rings (ideals).