Partial regularities and $a^*$-invariants of Borel type ideals

TL;DR

This paper investigates the properties of partial regularities and $a^*$-invariants of Borel type ideals, expressing them via irreducible decompositions and analyzing their behavior under algebraic operations.

Contribution

It introduces formulas for invariants of Borel type ideals based on irreducible decompositions and studies their behavior under intersections and sums.

Findings

Expressed partial regularities and $a^*$-invariants in terms of irreducible decompositions.

Analyzed the behavior of these invariants under intersections.

Analyzed the behavior of these invariants under sums.

Abstract

We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.