On Near Armendariz Ideals

Khadijeh Khalilnezhad, Hamid Haj Seyyed Javadi


‎We say a left ideal $I$ is a near Armendariz whenever polynomials‎

‎$(x) f = f_0‎ + ‎f_1 x‎ + ‎\ldots‎ + ‎f_m x^m$‎, ‎$(x) g = g_0‎ + ‎g_1 x‎ + ‎\ldots‎ + ‎g_n x^n \in R [x]$ satisfy $(x) f o (x)g \in r_{R[x]}(I[x])$ then $ g_j f_i\in r_{R}(I)$ for each $1\leq i \leq m$‎, ‎$1\leq j \leq n$ and $(f_0)g\in r_{R}(I)$‎.

‎The behavior of the left near Armendariz ideal condition is\linebreak investigated with respect to various constructions‎. ‎It is shown that every left ideal of a near Armendariz ring is a near Armendariz left ideal‎. ‎Examples are included to illustrate and delimit the theory‎.



Full Text: PDF


  • There are currently no refbacks.

The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|