Open Access$\tau$-Atomicity and Quotients of Size Four
Author(s) -
Richard Erwin Hasenauer,
Bethany Kubik
Publication year - 2021
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.52.2021.3241
Subject(s) - atomicity , factorization , mathematics , quotient , lambda , ideal (ethics) , unit (ring theory) , combinatorics , element (criminal law) , ring (chemistry) , discrete mathematics , computer science , physics , chemistry , algorithm , law , mathematics education , programming language , database transaction , organic chemistry , political science , optics
Given a ring $R$, an ideal $I$ of $R$, and an element $a\in I$, we say $a=\lambda b_1\cdots b_k$ is a $\tau_I$-factorization of $a$ if $\lambda$ is any unit and $b_1\equiv\cdots\equiv b_k\pmod{I}$. In this paper, we investigate the $\tau_I$-atomicity of PIDs with ideals where $R/I$ has size four.