SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]

Title & Authors
SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]
Woo, Sung-Sik;

Abstract
In [2], they found some natural generators for the ideals of the finite ring $\small{Z_{pm}}$[X]/$\small{(X^n\;-\;1)}$, where p and n are relatively prime. If p and n are not relatively prime $\small{X^n\;-\;1}$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $\small{Z_{pm}}$[X]/$\small{(X^n\;-\;1)}$ in 'inseparable' case we need to look at the primary ideals of $\small{Z_{pm}}$[X]. In this paper, we find a set of generators of ideals of $\small{Z_{pm}}$[X]/(f) for some primary polynomials f of $\small{Z_{pm}}$[X].돀飶�⨀肴�⨀䀈�⨀惾�⨀�덐烾�⨀�렄룹�⨀Ā蠉顏㒔Ā仒ﺿ缀ȀĀ砾җ⨀ꃻ�⨀젾җ⨀ꡠ஗⨀აⶓ硪̗లȀĀ᣻�⨀Ѐ㠳җ⨀Ā恿ಗ⨀䄀ᠸҗ⨀骴쁗麴ࠀ̀硪̗లȀ뀵җ⨀ꀸҗ⨀Ā졝�⨀ၡ�⨀袨ɠ悸硛�⨀ꢇ媸섂돀想�⨀堘�⨀肴�⨀塤ಗ⨀餂돐D᪗⨀墵�⨀／ࠀ衤ಗ⨀夂덐栀 ⠀�䪓硪̗లȀĀ壽�⨀Ѐꣳ�⨀Āﲖ⨀䄀頲җ⨀骴쁗麴ࠀ̀硪̗లȀ⃶�⨀″җ⨀Ā졝�⨀ၡ�⨀袨ɠ悸硛�⨀ꢇ媸�⨀
Keywords
primary ideal;polynomial over a finite ring;
Language
English
Cited by
References
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M. Atiyah, Addison-Wesley (1965)

2.
P. Kanwar and Sergio, Cyclic codes over integer modulo \$p^n\$, finite fields and their applications 3(2) (1997)

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S. Lang, Algebra, 3rd ed., Addison Wesley, 1993

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B. R. McDonalds, Finite rings with identity, Dekker, New York, 1974