$\tau$-Atomicity and Quotients of Size Four | Zendy

Richard Erwin Hasenauer | Zendy; Bethany Kubik | Zendy

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$\tau$-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.

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