2023/12/15 by Hager, Rico, Hamel, Andreas H, Heyde, Frank
#20M10 #20M12 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2312.09914
Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive elements, minimal ideals and simple semigroups all with respect to a given ideal. An application to set optimization is discussed.