3 research outputs found
A note on unitizations of generalized effect algebras
There is a forgetful functor from the category of generalized effect algebras
to the category of effect algebras. We prove that this functor is a right
adjoint and that the corresponding left adjoint is the well-known unitization
construction by Hedl\'ikov\'a and Pulmannov\'a. Moreover, this adjunction is
monadic
Unitizations of generalized pseudo effect algebras and their ideals
A generalized pseudo effect algebra (GPEA) is a partially ordered partial
algebraic structure with a smallest element 0, but not necessarily with a unit
(i.e, a largest element). If a GPEA admits a so-called unitizing automorphism,
then it can be embedded as an order ideal in its so-called unitization, which
does have a unit. We study unitizations of GPEAs with respect to a unitizing
automorphism, paying special attention to the behavior of congruences and
ideals in this setting.Comment: 30 page
Discrete -valued states and -perfect pseudo-effect algebras
We give sufficient and necessary conditions to guarantee that a pseudo-effect
algebra admits an -valued discrete state. We introduce -perfect
pseudo-effect algebras as algebras which can be split into comparable
slices. We prove that the category of strong -perfect pseudo-effect algebras
is categorically equivalent to the category of torsion-free directed partially
ordered groups of a special type