عنوان مجله
|
Journal of Algebraic Systems
|
چکیده
|
In this paper, we study the categorical and algebraic
properties, such as limits and colimits of the category Pos-S with
respect to order dense embeddings. Injectivity with respect to this
class of monomorphisms has been studied by the author and used
to obtain information about injectivity relative to order embeddings.
Then, we study three different kinds of essentiality, usually
used in literature, with respect to the class of all order dense embeddings
of S-posets, and investigate their relations to order dense
injectivity. We will see, among other things, that although all of
these essential extensions are not necessarily equivalent, they behave
equivalently with respect to order dense injectivity. More
precisely, it is proved that order dense injectivity well behaves regarding
these essentialities. Finally, a characterization of these
essentialities over pogroups is given.
|