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Generalized state maps and states on pseudo equality algebras

Generalized state maps and states on pseudo equality algebras AbstractIn this paper, we attempt to cope with states in a universal algebraic setting, that is, introduce a notion of generalized state map from a pseudo equality algebra X to an arbitrary pseudo equality algebra Y. We give two types of special generalized state maps, namely, generalized states and generalized internal states. Also, we study two types of states, namely, Bosbach states and Riečan states. Finally, we discuss the relations among generalized state maps, states and internal states (or state operators) on pseudo equality algebras. We verify the results that generalized internal states are the generalization of internal states, and generalized states are the generalization of state-morphisms on pseudo equality algebras. Furthermore, we obtain that generalized states are the generalization of Bosbach states and Riečan states on linearly ordered and involutive pseudo equality algebras, respectively. Hence we can come to the conclusion that, in a sense, generalized state maps can be viewed as a possible united framework of the states and the internal states, the state-morphisms and the internal state-morphisms on pseudo equality algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

Generalized state maps and states on pseudo equality algebras

Open Mathematics , Volume 16 (1): 16 – Mar 2, 2018

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Publisher
de Gruyter
Copyright
© 2018 Cheng et al., published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
DOI
10.1515/math-2018-0014
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we attempt to cope with states in a universal algebraic setting, that is, introduce a notion of generalized state map from a pseudo equality algebra X to an arbitrary pseudo equality algebra Y. We give two types of special generalized state maps, namely, generalized states and generalized internal states. Also, we study two types of states, namely, Bosbach states and Riečan states. Finally, we discuss the relations among generalized state maps, states and internal states (or state operators) on pseudo equality algebras. We verify the results that generalized internal states are the generalization of internal states, and generalized states are the generalization of state-morphisms on pseudo equality algebras. Furthermore, we obtain that generalized states are the generalization of Bosbach states and Riečan states on linearly ordered and involutive pseudo equality algebras, respectively. Hence we can come to the conclusion that, in a sense, generalized state maps can be viewed as a possible united framework of the states and the internal states, the state-morphisms and the internal state-morphisms on pseudo equality algebras.

Journal

Open Mathematicsde Gruyter

Published: Mar 2, 2018

Keywords: Pseudo equality algebra; Generalized state map; Bosbach state; Rie č an state; Internal state; 03G25; 06F99

References