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On state pseudo-hoops
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AbstractRecently, the bounded pseudo-hoops with internal states have been defined and studied. Some of results are based on the hypothesis that a bounded pseudo-hoop has the Glivenko and (mN) properties. In this paper we show that this hypothesis is superfluous, namely every good pseudo-hoop satisfies the Glivenko and (mN) properties and those results are reformulated without that hypothesis. The pointed pseudo-hoops are introduced and studied and the notion of state operator has been generalized for the case of unbounded pseudo-hoops. We define the Bosbach and Riečan states on pointed pseudo-hoops and we make some considerations regarding the relationship between the state operators and states on these structures.
Title: On state pseudo-hoops
Description:
AbstractRecently, the bounded pseudo-hoops with internal states have been defined and studied.
Some of results are based on the hypothesis that a bounded pseudo-hoop has the Glivenko and (mN) properties.
In this paper we show that this hypothesis is superfluous, namely every good pseudo-hoop satisfies the Glivenko and (mN) properties and those results are reformulated without that hypothesis.
The pointed pseudo-hoops are introduced and studied and the notion of state operator has been generalized for the case of unbounded pseudo-hoops.
We define the Bosbach and Riečan states on pointed pseudo-hoops and we make some considerations regarding the relationship between the state operators and states on these structures.
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