Weak differences, weak BCK-algebras and applications to some partial orders on rings
-
Insa Cremer
and
Janko Marovt
Abstract
This article introduces a weak difference on a poset as a generalization of a difference on a poset and deals with connections between weak differences and weak BCK-algebras. In particular, conditions under which a poset with a certain weak difference is a meet semilattice are provided. These conditions are then applied to some partial orders on rings, namely the weak right star order and the strong right star order on a right-strong Rickart ring, as well as the sharp order on a certain subset of an arbitrary unitary ring.
Acknowledgement
The authors wish to thank Jānis Cīrulis for sharing his expertise and advice.
(Communicated by Mirko Navara)
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Articles in the same Issue
- Weak differences, weak BCK-algebras and applications to some partial orders on rings
- Weakly κ-compact topological spaces
- On sharp radius estimates for S*(β) and a product function
- Maximal subextension and stability in m-capacity of maximal subextension of m-subharmonic functions with given boundary values
- Asymptotic behavior of fractional super-linear differential equations
- New and improved oscillation criteria of third-order half-linear delay differential equations via canonical transform
- Global dynamics of the system of difference equations
- Results on oscillatory properties of third-order functional difference equations with semi-canonical operators
- A new approach to metrical fixed point theorems
- Generalized Baker’s result and stability of functional equations using fixed point results
- Characterizations of ℕ-compactness and realcompactness via ultrafilters in the absence of the axiom of choice
- K-theory of oriented flag manifolds
- On certain observations on split continuity and cauchy split continuity
- On the generalized eta- and theta-transformation formulas as the Hecke modular relation
- On some selective star Lindelöf-type properties
