Geodesic
A morphic ring of neat range one
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 325-329

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We show that a commutative ring $R$ has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring $R$ has a neat range one if and only if for any elements $a, b \in R$ such that $aR=bR$ there exist neat elements $s, t \in R$ such that $bs=c$, $ct=b$. Examples of morphic rings of neat range one are given.
Keywords: Bezout ring, neat ring, clear ring, elementary divisor ring, stable range one, neat range one. 
@article{ADM_2015_20_2_a9,
     author = {O. Pihura and B. Zabavsky},
     title = {A morphic ring of neat range one},
     journal = {Algebra and discrete mathematics},
     pages = {325--329},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a9/}
}
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O. Pihura; B. Zabavsky. A morphic ring of neat range one. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 325-329. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a9/