Geodesic
Partial orders based on inverses along elements
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 58-80

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The paper introduces and investigates partial orders that are finer than the minus partial order and are based on inverses along an element and other specific outer inverses. It turns out that in this way a number of classical partial orders can be equivalently defined. 
@article{ZNSL_2017_463_a5,
     author = {A. Guterman and X. Mary and P. Shteyner},
     title = {Partial orders based on inverses along elements},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {58--80},
     publisher = {mathdoc},
     volume = {463},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a5/}
}
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A. Guterman; X. Mary; P. Shteyner. Partial orders based on inverses along elements. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 58-80. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a5/