On n-Absorbing Ideals and Two Generalizations of Semiprime Ideals

Hojjat Mostafanasab, Ahmad Yousefian Darani

Abstract


Let R be a commutative ring and n be a positive integer. A proper ideal I of R is called an n-absorbing ideal if whenever x_1...x_{n+1}\in I for x_1,...,x_{n+1}\in R, then there are n of the x_i's whose product is in I. We give a generalization of Prime Avoidance Theorem. Also, an n-Absorbing Avoidance Theorem is proved. Moreover, we introduce the notions of quasi-n-absorbing ideals and of semi-n-absorbing ideals. We say that a proper ideal I of R is a quasi-n-absorbing ideal if whenever a^nb\in I for a,b\in R, then a^n\in I or a^{n-1}b\in I. A proper ideal I of R is said to be a semi-n-absorbing ideal if whenever a^{n+1}\in I for a\in R, then a^n\in I.

Full Text: PDF

Refbacks

  • 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|