Geodesic
Matrix theory over ringoids
Filomat, Tome 37 (2023) no. 30, p. 10275

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DOI

We will study the notion of right distributive ringoids over a field which are neither rings, semi-rings, semi-hyperrings nor near-rings. Matrices over ringoids are defined, and new concepts such as top-row-determinate and down-row-determinate related to 2 × 2 matrices over a ringoid are introduced. Moreover, we investigate the notions of the (strongly, (very-) weak) orthogonality of vectors over a ringoid. Beside, we discuss the notion of incident vectors and define the concept of α − K-sphere on a ringoid, where K is a field and investigate some of their properties. Finally, we show that in a commutative ringoid all of the vectors are strongly orthogonal.
DOI : 10.2298/FIL2330275R
Classification : 20N02, 20N99, 11E81
Keywords: Left zero, (right-) distributive) ringoid, (Linear) groupoid, (Strongly, (very-) weak) orthogonal 
Akbar Rezaei; Hee Sik Kim; Rajab Ali Borzooei; Arsham Boru; and Saeid. Matrix theory over ringoids. Filomat, Tome 37 (2023) no. 30, p. 10275 . doi: 10.2298/FIL2330275R
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     title = {Matrix theory over ringoids},
     journal = {Filomat},
     pages = {10275 },
     year = {2023},
     volume = {37},
     number = {30},
     doi = {10.2298/FIL2330275R},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2330275R/}
}
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