Monoids in proximal Banach spaces
J. F. Peters, Ebubeki̇r İnan, Mehmet Ali̇ Öztürk · International Journal of Algebra · 2014
Copyright c © 2014 J.F. Peters, E. İnan and M.A. Öztürk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Given the binary operation ◦δ: 2V ×2V − → 2V defined on a subset of 2V in the proximal Banach space V, we prove that the monoid S = 2V (◦δ) is regular, every right ideal A ⊂ S and left ideal B ⊂ S are proximal, every ideal in S is idempotent and S is simple. For A◦, B◦, C ◦ ∈ 2V (◦δ), we also prove that if ((A ◦ ◦δ B◦) ◦δ C◦) ◦δ D ◦ 6 = ∅, then D ◦ and at least