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Weak chain-completeness and fixed point property for pseudo-ordered sets

S. Parameshwara Bhatta (2005)

Czechoslovak Mathematical Journal

In this paper the notion of weak chain-completeness is introduced for pseudo-ordered sets as an extension of the notion of chain-completeness of posets (see [3]) and it is shown that every isotone map of a weakly chain-complete pseudo-ordered set into itself has a least fixed point.

Weighted w -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

Let R be a unital * -ring. For any a , s , t , v , w R we define the weighted w -core inverse and the weighted dual s -core inverse, extending the w -core inverse and the dual s -core inverse, respectively. An element a R has a weighted w -core inverse with the weight v if there exists some x R such that a w x v x = x , x v a w a = a and ( a w x ) * = a w x . Dually, an element a R has a weighted dual s -core inverse with the weight t if there exists some y R such that y t y s a = y , a s a t y = a and ( y s a ) * = y s a . Several characterizations of weighted w -core invertible and weighted dual s -core invertible...

Well-quasi-ordering Aronszajn lines

Carlos Martinez-Ranero (2011)

Fundamenta Mathematicae

We show that, assuming PFA, the class of all Aronszajn lines is well-quasi-ordered by embeddability.

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