Involutive equality algebras
The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a ( ∼ 0 ) -involutive subalgebra. We prove that each ( ∼ 0 ) -involutive...
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Published in | Soft computing (Berlin, Germany) Vol. 22; no. 22; pp. 7505 - 7517 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.11.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a
(
∼
0
)
-involutive subalgebra. We prove that each
(
∼
0
)
-involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define
(
∼
0
)
-involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a
(
∼
0
)
-involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras. |
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ISSN: | 1432-7643 1433-7479 |
DOI: | 10.1007/s00500-018-3032-1 |