The Radical Trace Property and Primary Ideals

The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals

For standard graded Artinian K-algebras defined by componentwise linear ideals and Gotzmann ideals, we give conditions for the weak Lefschetz property in terms of numerical invariants of the defining ideals.

Primary Ideals and Valuation Ideals

Radical of $cdot$-ideals in $PMV$-algebras

‎In this paper‎, ‎we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$‎. ‎Also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra‎. ‎Finally we show that $A/I$ has no nilpotent elemen...

Radical of Primary-like submodules satisfying the primeful property

In this article, we develop the tool of saturation in the context of primary-like submodules of modules. We are particularly interested in relationships among the saturation of a primary-like submodule satisfying the primeful property and its radical. Furthermore, we provide sufficient conditions involving saturation and torsion arguments under which the radical of such a submodule is prime.

Running-head: Theories, ideals, and property induction Theories, Ideals, and Category-Based Property Induction

One important property of human object categories is that they are the categories to which newly observed properties are likely to be generalized. Another is that such categories often exhibit theoretical coherence. This study examined the relationship between inductive generalization and theoretical coherence by manipulating the causal knowledge associated with novel categories and assessing t...