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## trenOn The Para-Octonions; a Non-Associative Normed AlgebraPara-Ktonyonlar Üzerine; Bir İlişkisel Olmayan Normlu Cebir

#### Mehdi JAFARI [1]

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In this paper, para-octonions and their algebraic properties are provided by using the Cayley-Dickson multiplication rule between the octonionic

basis elements. The trigonometric form of a para-octonion is similar to the trigonometric form of dual number and quasi-quaternion.

We study the De-Moivre’s theorem for para-octonions, extending results obtained for real octonions and defining generalize Euler’s

formula for para-octonions.

Bu çalışmada, octonyonik baz elemanları arasında Cayley-Dickson çarpım kuralı kullanılarak para-octonyonlar ve cebirsel özellikleri verilmiştir.

Bir para-octonyonun trigonometrik formu bir dual-sayının ve bir quasi-kuaterniyonun trigonometrik formuna benzerdir. Para-octonyonlar

içn De-Moivre’nin teoremi ele alınarak reel-octonyonlar için elde edilen sonuçlar genelleştirilmiştir. Ayrıca, para-octonyonlar

için genel Euler formülleri tanımlanmıştır.

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• Mortazaasl H., Jafari M., (2013). A study on Semi-quaternions Algebra in Semi-Euclidean 4-Space, Mathematical Sciences and Applications E-Notes, 1(2) 20-27.
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Konular Mühendislik Araştırma Makaleleri Yazar: Mehdi JAFARI
 Bibtex @ { marufbd290481, journal = {Marmara Fen Bilimleri Dergisi}, issn = {}, eissn = {2146-5150}, address = {Marmara Üniversitesi}, year = {2016}, volume = {28}, pages = {95 - 99}, doi = {10.7240/mufbed.36025}, title = {On The Para-Octonions; a Non-Associative Normed Algebra}, key = {cite}, author = {JAFARI, Mehdi} } APA JAFARI, M . (2016). On The Para-Octonions; a Non-Associative Normed Algebra. Marmara Fen Bilimleri Dergisi, 28 (3), 95-99. DOI: 10.7240/mufbed.36025 MLA JAFARI, M . "On The Para-Octonions; a Non-Associative Normed Algebra". Marmara Fen Bilimleri Dergisi 28 (2016): 95-99 Chicago JAFARI, M . "On The Para-Octonions; a Non-Associative Normed Algebra". Marmara Fen Bilimleri Dergisi 28 (2016): 95-99 RIS TY - JOUR T1 - On The Para-Octonions; a Non-Associative Normed Algebra AU - Mehdi JAFARI Y1 - 2016 PY - 2016 N1 - doi: 10.7240/mufbed.36025 DO - 10.7240/mufbed.36025 T2 - Marmara Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 95 EP - 99 VL - 28 IS - 3 SN - -2146-5150 M3 - doi: 10.7240/mufbed.36025 UR - http://dx.doi.org/10.7240/mufbed.36025 Y2 - 2016 ER - EndNote %0 Marmara Fen Bilimleri Dergisi On The Para-Octonions; a Non-Associative Normed Algebra %A Mehdi JAFARI %T On The Para-Octonions; a Non-Associative Normed Algebra %D 2016 %J Marmara Fen Bilimleri Dergisi %P -2146-5150 %V 28 %N 3 %R doi: 10.7240/mufbed.36025 %U 10.7240/mufbed.36025 ISNAD JAFARI, Mehdi . "On The Para-Octonions; a Non-Associative Normed Algebra". Marmara Fen Bilimleri Dergisi 28 / 3 (Aralık 2017): 95-99. http://dx.doi.org/10.7240/mufbed.36025