Why most papers on filters are really trivial (including this one)

TL;DR

This paper argues that many research papers on filters in residuated structures are trivial, as their results are simple consequences of well-known, more general theorems, highlighting a need for more substantial contributions.

Contribution

It demonstrates that numerous filter-related results in residuated structures are not novel but are straightforward corollaries of existing, established theorems.

Findings

Many filter papers are trivial consequences of known results

The paper clarifies the redundancy in existing literature

Encourages more meaningful research contributions

Abstract

The aim of this note is to show that many papers on various kinds of filters (and related concepts) in (subreducts of) residuated structures are in fact easy consequences of more general results that have been known for a long time.