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- 학술저널
- 저자정보
- 저널정보
- 원광대학교 기초자연과학연구소 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.28 No.1
- 발행연도
- 2024.8
- 수록면
- 85 - 104 (20page)
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In this paper, we relate a bounded semihoop $ A $ to an abelian $ \ell $-group $ G $ to study $ G $-states. Firstly, the notion of Bosbach $ G $-states on bounded semihoops is presented, which reflects a certain characteristic of energy conservation. We also obtain some important conclusions of Bosbach $ G $-state as follows: $ (1) $ Let $ s $ be a Bosbach $ G $-state on a bounded semihoop $ A $ and $ H $ be a down-set subgroup of $ G $. Then $ s^{-1}(H) $ is an ideal of $ A $. $ (2) $ Every bounded dual perfect semihoop has a non-zero Bosbach $ G $-state. Secondly, we propose the notion of Rie$\check{c}$an $ G $-states on bounded semihoops and obtain some properties. We prove that every Bosbach $ G $-state is a Rie$\check{c}$an $ G $-state on a bounded semihoop $ A $ but a Rie$\check{c}$an $ G $-state may not be a Bosbach $ G $-state unless $ A $ has the DNP property. Finally, we introduce the concept of $ G $-state morphisms and obtain some characterizations of $ G $-state morphisms.
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