Geodesic
EP elements of Z[x]/(x 2 + x)
Filomat, Tome 37 (2023) no. 22, p. 7467

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DOI

In this paper, we first show that the quotient ring Z[x]/(x 2 + x) is an involution-ring with the involution * given by (a 1 + a 2 x) * = a 1 − a 2 − a 2 x, where a 1 , a 2 ∈ Z. Then, we determine explicitly all invertible elements, regular elements, MP-inverses, group invertible elements, EP elements and SEP elements of Z[x]/(x 2 + x). Furthermore, we give a new characterization for Abel rings.
DOI : 10.2298/FIL2322467C
Classification : 13B25, 16U90
Keywords: Moore-Penrose inverse, Group invertible element, EP element, Polynomial ring, Abel ring 
Liufeng Cao; Lan You; Junchao Wei. EP elements of Z[x]/(x 2 + x). Filomat, Tome 37 (2023) no. 22, p. 7467 . doi: 10.2298/FIL2322467C
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     author = {Liufeng Cao and Lan You and Junchao Wei},
     title = {EP elements of {Z[x]/(x} 2 + x)},
     journal = {Filomat},
     pages = {7467 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322467C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322467C/}
}
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