MORPHIC PROPERTY OF A QUOTIENT RING OVER POLYNOMIAL RING

Title & Authors
MORPHIC PROPERTY OF A QUOTIENT RING OVER POLYNOMIAL RING
Long, Kai; Wang, Qichuan; Feng, Lianggui;

Abstract
A ring R is called left morphic if $\small{R/Ra{\simeq_-}l(a)}$ for every $\small{a{\in}R}$. Equivalently, for every $\small{a{\in}R}$ there exists $\small{b{\in}R}$ such that $\small{Ra=l(b)}$ and $\small{l(a)=Rb}$. A ring R is called left quasi-morphic if there exist $\small{b}$ and $\small{c}$ in R such that $\small{Ra=l(b)}$ and $\small{l(a)=Rc}$ for every $\small{a{\in}R}$. A result of T.-K. Lee and Y. Zhou says that R is unit regular if and only if $\small{R[x}$$\small{]}$$\small{/(x^2){\simeq_-}R{\propto}R}$ is morphic. Motivated by this result, we investigate the morphic property of the ring $\small{S_n=^{def}R[x_1,x_2,{\cdots},x_n}$$\small{]}$$\small{/(\{x_ix_j\})}$, where $\small{i,j{\in}\{1,2,{\cdots},n\}}$. The morphic elements of $\small{S_n}$ are completely determined when R is strongly regular.
Keywords
morphic property;polynomial ring;strongly regular;
Language
English
Cited by
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