Geodesic
The p-semisimple property for some generalizations of BCI algebras and its applications
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 79-94.

Voir la notice de l'article provenant de la source Library of Science

This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.
Keywords: RM/tRM/*RM/RM**/*aRM/BCI/BCH/BZ/pre-BZ/pre-BCI algebras, p-semisimplicity, mereology, antisymmetry 
@article{AUPCM_2020_19_a6,
     author = {Obojska, Lidia and Walendziak, Andrzej},
     title = {The p-semisimple property for some generalizations of {BCI} algebras and its applications},
     journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
     pages = {79--94},
     publisher = {mathdoc},
     volume = {19},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a6/}
}
TY  - JOUR
AU  - Obojska, Lidia
AU  - Walendziak, Andrzej
TI  - The p-semisimple property for some generalizations of BCI algebras and its applications
JO  - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY  - 2020
SP  - 79
EP  - 94
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a6/
LA  - en
ID  - AUPCM_2020_19_a6
ER  - 
%0 Journal Article
%A Obojska, Lidia
%A Walendziak, Andrzej
%T The p-semisimple property for some generalizations of BCI algebras and its applications
%J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
%D 2020
%P 79-94
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a6/
%G en
%F AUPCM_2020_19_a6
Obojska, Lidia; Walendziak, Andrzej. The p-semisimple property for some generalizations of BCI algebras and its applications. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 79-94. http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a6/

[1] Aslam, Muhammad, and Allah-Bakhsh Thaheem. "A note on p-semisimple BCIalgebras." Math. Japon. 36, no. 1 (1991): 39-45.

[2] Clay, Robert Edward. "Relation of Lesniewski’s mereology to Boolean algebra." J. Symbolic Logic 39 (1974): 638-648.

[3] Hoo, Cheong Seng. "Closed ideals and p-semisimple BCI-algebras." Math. Japon. 35, no. 6 (1990): 1103-1112.

[4] Hu, Qing Ping, and Xin Li. "On BCH-algebras." Math. Sem. Notes Kobe Univ. 11, no. 2 (1983): 313-320.

[5] Imai, Yasuyuki, and Kiyoshi Iséki. "On axiom systems of propositional calculi. XIV." Proc. Japan Acad. 42 (1966): 19-22.

[6] Iorgulescu, Afrodita. "New generalizations of BCI, BCK and Hilbert algebras – Part I." J. Mult.-Valued Logic Soft Comput. 27, no. 4 (2016): 353-406.

[7] Iorgulescu, Afrodita. "New generalizations of BCI, BCK and Hilbert algebras – Part II." J. Mult.-Valued Logic Soft Comput. 27, no. 4 (2016): 407-456.

[8] Iséki, Kiyoshi. "An algebra related with a propositional calculus." Proc. Japan Acad. 42 (1966): 26-29.

[9] Kim, Hee Sik, and Hong Goo Park. "On 0-commutative B-algebras." Sci. Math. Jpn. 62, no. 1 (2005): 7-12.

[10] Lei, Tian De, and Chang Chang Xi. "p-radical in BCI-algebras." Math. Japon. 30, no. 4 (1985): 511-517.

[11] Lesniewski, Stanisław. Stanislaw Lesniewski: Collected Works - Volumes I and II. Vol. 44 of Nijhoff International Philosophy Series. Dordrecht: Kluwer Academic Publishers, 1992.

[12] Loeb, Iris. "From Mereology to Boolean Algebra: The Role of Regular Open Sets in Alfred Tarski’s Work." In: The History and Philosophy of Polish Logic: Essays in Honour of Jan Wolenski, 259-277. New York: Palgrave Macmillan, 2014.

[13] Meng, Dao Ji. "BCI-algebras and abelian groups." Math. Japon. 32, no. 5 (1987): 693-696.

[14] Obojska, Lidia. "Some remarks on supplementation principles in the absence of antisymmetry." Rev. Symb. Log. 6, no. 2 (2013): 343-347.

[15] Obojska, Lidia. U zródeł zbiorów kolektywnych: o mereologii nieantysymetrycznej. Siedlce: Wydawnictwo UPH, 2013.

[16] Patrignani, Claudia et al. (Particle Data Group). "Review of Particle Physics." Chin. Phys. C 40, no. 10 (2016): 100001.

[17] Pietruszczak, Andrzej. Metamereologia. Torun: Wydawnictwo Naukowe Uniwersytetu Mikołaja Kopernika, 2000.

[18] Shohani, Javad, Rajab Ali Borzooei, and Morteza Afshar Jahanashah. "Basic BCI-algebras and abelian groups are equivalent." Sci. Math. Jpn. 66, no. 2 (2007): 243-245.

[19] Walendziak, Andrzej. "On BF-algebras." Math. Slovaca 57, no. 2 (2007): 119-128.

[20] Ye, Reifen. "On BZ-algebras." In: Selected paper on BCI/BCK-algebras and Computer Logics, 21-24. Shaghai: Shaghai Jiaotong University Press, 1991.

[21] Zhang, Qun. "Some other characterizations of p-semisimple BCI-algebras." Math. Japon. 36, no. 5 (1991): 815-817.