We show that a zerosymmetric nearring $N$ is left regular if and only if $N $ is regular and isomorphic to a subdirect product of integral nearrings, where each component is either an AnshelClay nearring or a trivial integral nearring. We also show that a zerosymmetric nearring is regular without nonzero nilpotent elements if and only if the multiplicative semigroup of N is a union of disjoint groups.
Primary Language  en 

Subjects  Mathematics 
Journal Section  Articles 
Authors 

Bibtex  @research article { ujma469745,
journal = {Universal Journal of Mathematics and Applications},
issn = {26199653},
address = {Emrah Evren KARA},
year = {2019},
volume = {2},
pages = {11  13},
doi = {10.32323/ujma.469745},
title = {A Characterization of Left Regularity},
key = {cite},
author = {Fuchs, Peter}
} 
APA  Fuchs, P . (2019). A Characterization of Left Regularity. Universal Journal of Mathematics and Applications, 2 (1), 1113. DOI: 10.32323/ujma.469745 
MLA  Fuchs, P . "A Characterization of Left Regularity". Universal Journal of Mathematics and Applications 2 (2019): 1113 <http://dergipark.org.tr/ujma/issue/44032/469745> 
Chicago  Fuchs, P . "A Characterization of Left Regularity". Universal Journal of Mathematics and Applications 2 (2019): 1113 
RIS  TY  JOUR T1  A Characterization of Left Regularity AU  Peter Fuchs Y1  2019 PY  2019 N1  doi: 10.32323/ujma.469745 DO  10.32323/ujma.469745 T2  Universal Journal of Mathematics and Applications JF  Journal JO  JOR SP  11 EP  13 VL  2 IS  1 SN  26199653 M3  doi: 10.32323/ujma.469745 UR  https://doi.org/10.32323/ujma.469745 Y2  2018 ER  
EndNote  %0 Universal Journal of Mathematics and Applications A Characterization of Left Regularity %A Peter Fuchs %T A Characterization of Left Regularity %D 2019 %J Universal Journal of Mathematics and Applications %P 26199653 %V 2 %N 1 %R doi: 10.32323/ujma.469745 %U 10.32323/ujma.469745 
ISNAD  Fuchs, Peter . "A Characterization of Left Regularity". Universal Journal of Mathematics and Applications 2 / 1 (March 2019): 1113. https://doi.org/10.32323/ujma.469745 