Partial Orders Based on Inverses Along Elements

Guterman, Alexander; Mary, Xavier; Shteyner, Pavel

doi:10.1007/s10958-018-3908-8

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2021

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“…This notion generalizes all classical outer inverses and unifies many classical notions connected to generalized inverses. In particular, partial order relations on semigroups such as Nambooripad order, sharp order, star order and others, can be defined in terms of outer inverses, see [11,12].…”

Section: Introductionmentioning

confidence: 99%

Ordering Orders and Quotient Rings

Guterman

Márki

Shteyner

2021

Springer Proceedings in Mathematics &Amp; Statistics

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In the present paper, we introduce a general notion of quotient ring which is based on inverses along an element. We show that, on the one hand, this notion encompasses quotient rings constructed using various generalized inverses. On the other hand, such quotient rings can be viewed as Fountain-Gould quotient rings with respect to appropriate subsets. We also investigate the connection between partial order relations on a ring and on its ring of quotients.

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Section: Introductionmentioning

confidence: 99%