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Results in L-algebras
Algebra universalis ( IF 0.6 ) Pub Date : 2021-01-04 , DOI: 10.1007/s00012-020-00695-1
Lavinia Corina Ciungu

We study some classes of L-algebras and we give characterizations of commutative KL-algebras and CL-algebras. It is proved that any commutative KL-algebra is a BCK-algebra and any self-similar CL-algebra is commutative. The commutative ideals are defined and studied, and it is proved that a CL-algebra is commutative if and only if all its ideals are commutative. We also present the L-algebras arising from other structures, such as BCK-algebras, pseudo MV-algebras, pseudo BL-algebras, pseudo-hoops, bounded R\(\ell \)-monoids, BE-algebras, Hilbert algebras.



中文翻译:

L-代数的结果

我们研究了一些L代数,并给出了可交换KL代数和CL代数的特征。证明了任何可交换的KL-代数都是BCK-代数,任何自相似的CL-代数都是可交换的。定义和研究了交换理想,并且证明了CL-代数在且仅当所有理想都是可交换的时才是可交换的。我们还介绍了源自其他结构的L代数,例如BCK代数,伪MV代数,伪BL代数,伪箍,有界R \(\ ell \)-类群,BE代数,希尔伯特代数。

更新日期:2021-01-05
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