Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Local and perfect CL -algebras. |
| Συγγραφείς: |
Liang, Jie1 (AUTHOR), Borzooei, R A1 (AUTHOR), Kologani, M Aaly2 (AUTHOR) |
| Πηγή: |
Logic Journal of the IGPL. Oct2026, Vol. 34 Issue 5, p1-33. 33p. |
| Θεματικοί όροι: |
Boolean algebra, Ideals (Algebra) |
| Περίληψη: |
This paper mainly focus on investigating local |$L$| -algebras and giving some characterizations of different local |$L$| -algebras. To begin with, we introduce the concept of local |$L$| -algebras and give some characterizations of bounded local |$CL$| -algebras by the order of element and primary ideals, respectively. We then investigate perfect |$L$| -algebras and prove that each bounded local |$CL$| -algebra |$L$| is perfect if and only if the quotient |$L$| -algebra determined by some ideal of |$L$| is isomorphic to a Boolean algebra. Furthermore, we study the locally finite |$L$| -algebras and obtain that each quotient |$L$| -algebra determined by an ideal of any bounded |$CL$| -algebra is locally finite if and only if such ideal is maximal. In addition, we prove that every local bounded |$CL$| -algebra belongs exactly to one of the classes: perfect, locally finite, or peculiar. Lastly, we introduce the notion of |$CML$| -algebras and prove that each |$CML$| -algebra |$L$| is local, perfect, or locally finite if and only if the |$MV$| -center |$M(L)$| is a local, perfect, or locally finite |$MV$| -algebra, respectively. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: |
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