Research Information System
AXIOMS, vol.23, no.1, 2024 (SCI-Expanded)
In this study, we introduce the notion of the T-irreducible element as a generalization of the notion of the meet-irreducible element in complete lattices. We derive some related properties of these elements and T-prime elements. We prove that T-irreducible elements and T-prime elements are preserved under the isomorphism that is generated by the same t-norm. We discuss the relationship between the sets of T-prime elements and co-atoms under some conditions. We illustrate this discussion with some examples. We also give some characterizations for the sets of T-irreducible elements and T-prime elements on the direct product of lattices. Then, we show that Theorem 2 given by Karacal and Sagiroglu is false by giving some counterexamples. We present a necessary and sufficient condition for the mentioned theorem to be correct.