@article{Mekera_Yeşil_2024, title={A source of semiprimeness on inverse and completely regular semigroups}, volume={76}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7699}, DOI={10.3842/umzh.v76i8.7699}, abstractNote={<p>UDC 512.5</p> <p>We define $|S_{S}|$-inverse semigroup and $|S_{S}|$-completely regular semigroup structures that are not encountered in the literature and are studied in our work for the first time.<span class="Apple-converted-space"> </span>The properties of these new semigroup types and their relations with the other semigroup types, such as $|S_{S}|$-idempotent, $|S_{S}|$-regular, $|S_{S}|$-nonzero, and $|S_{S}|$-reduced semigroups, are discussed. Further, the relationship between the source of semiprimeness and the semiprime ideal is analyzed. It is also shown that the intersection of all semiprime ideals is equal to the source of semiprimeness.<span class="Apple-converted-space"> </span>Moreover, if a function is surjective, then it can be shown that the analyzed two structures are preserved under homomorphism.</p>}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Mekera, Rasie and Yeşil, Didem}, year={2024}, month={Sep.}, pages={1254 - 1259} }