A note on maximal $$\hbox {B}_p$$ -subalgebras of B-algebras

Afrika Matematika - Tập 34 Số 1 - Trang 1-7 - 2023
Endam, Joemar1
1Department of Mathematics, Negros Oriental State University, Dumaguete, Philippines

Tóm tắt

Using the results about maximal $$\hbox {B}_p$$ -subalgebras, we show that there are no noncommutative B-simple B-algebras of the following orders: (i) between 1 and 24, (ii) between 24 and 36, and (iii) between 36 and 60.

Tài liệu tham khảo

citation_journal_title=Sci. Math. Jpn.; citation_title=B-algebras and groups; citation_author=PJ Allen, J Neggers, HS Kim; citation_volume=9; citation_publication_date=2003; citation_pages=159-165; citation_id=CR1 citation_journal_title=Afr. Mat.; citation_title=On finite B-algebra; citation_author=R Ameri, A Borumand Saied, SA Nematolah Zadeh, A Radfar, RA Borzooei; citation_volume=26; citation_publication_date=2015; citation_pages=825-847; citation_doi=10.1007/s13370-014-0249-8; citation_id=CR2 citation_journal_title=Int. J. Algebra; citation_title=Lagrange’s theorem for B-algebras; citation_author=JS Bantug, JC Endam; citation_volume=11; citation_publication_date=2017; citation_pages=15-23; citation_doi=10.12988/ija.2017.616; citation_id=CR3 Bantug, J.S., Endam, J.C.: Maximal $$\text{B}_p$$ -subalgebras of B-algebras. Discuss. Math. Gen. Algebra Appl. 40, 25–36 (2020) citation_journal_title=Quasigroups Relat. Syst.; citation_title=On B-algebras and quasigroups; citation_author=JR Cho, HS Kim; citation_volume=8; citation_publication_date=2001; citation_pages=1-6; citation_id=CR5 citation_journal_title=Appl. Math. Sci.; citation_title=The second isomorphism theorem for B-algebras; citation_author=JC Endam, JP Vilela; citation_volume=8; citation_publication_date=2014; citation_pages=1865-1872; citation_id=CR6 citation_journal_title=Sci. Math. Jpn.; citation_title=Centralizer and Normalizer of B-algebras; citation_author=JC Endam; citation_volume=81; citation_issue=1; citation_publication_date=2018; citation_pages=17-23; citation_id=CR7 Endam, J.C., Banagua, E.C.: B-algebras acting on sets. Sci. Math. Jpn. 2, 1–7 (2018) citation_journal_title=Int. Math. Forum; citation_title=Some properties of cyclic B-algebras; citation_author=JC Endam, RC Teves; citation_volume=11; citation_publication_date=2016; citation_pages=387-394; citation_doi=10.12988/imf.2016.6111; citation_id=CR9 Endam, J.C., Bantug, J.S.: Cauchy’s theorem for B-algebras. Sci. Math. Jpn. 82(3), 221–228 (2019) citation_journal_title=Appl. Math. Sci.; citation_title=On cyclic B-algebras; citation_author=NC Gonzaga, JP Vilela; citation_volume=9; citation_publication_date=2015; citation_pages=5507-5522; citation_id=CR11 Kim, H.S., Park, H.G.: On 0-commutative B-algebras. Sci. Math. Jpn. 62(1), 7–12 (2005) Mamhot, A.A., Endam, J.C.: On $$\text{ B}_{{po}}$$ -algebras. Afr. Mat. 30(7–8), 1237–1248 (2019) citation_journal_title=Mat. Vesnik; citation_title=On B-algebras; citation_author=J Neggers, HS Kim; citation_volume=54; citation_publication_date=2002; citation_pages=21-29; citation_id=CR14 citation_journal_title=Int. Math. J.; citation_title=A fundamental theorem of B-homomorphism for B-algebras; citation_author=J Neggers, HS Kim; citation_volume=2; citation_publication_date=2002; citation_pages=207-214; citation_id=CR15 citation_journal_title=Afr. Mat.; citation_title=A note on automorphisms of finite B-algebras; citation_author=R Soleimani; citation_volume=29; citation_publication_date=2018; citation_pages=263-275; citation_doi=10.1007/s13370-017-0540-6; citation_id=CR16 citation_journal_title=Math. Slovaca; citation_title=Some axiomatizations of B-algebras; citation_author=A Walendziak; citation_volume=56; citation_issue=3; citation_publication_date=2006; citation_pages=301-306; citation_id=CR17 Walendziak, A.: A note on normal subalgebras in B-algebras. Sci. Math. Jpn. 62(1), 1–6 (2005)