Authors | H.Rasouli, H.Barzegar |
---|---|
Journal | Semigroup forum |
Page number | 186-197 |
Volume number | 92 |
Paper Type | Original Research |
Published At | 2016 |
Journal Grade | Scientific - research |
Journal Type | Typographic |
Journal Country | United States |
Abstract
For S a partially-ordered monoid (pomonoid), in this paper we consider
three variations of the notion of essentiality for regular monomorphisms of S-posets,
defining regular-essential, mono-essential and weakly regular-essential extensions of
S-posets. It is shown that, while the last two classes coincide and properly contain the
first, they all lead to the same notion of regular-injective envelope. Every S-poset has
such an envelope, and when S is a pogroup, it may be obtained by letting S act on the
MacNeille completion of the underlying poset.