THE DUAL OF A STRONGLY PRIME IDEAL

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JAHANINEZHAD R.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2010 | Volume:5 | Issue:1 Page(s): 19-26

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Information Journal Paper

Title

THE DUAL OF A STRONGLY PRIME IDEAL

Author(s)

JAHANINEZHAD R. | Issue Writer Certificate

Keywords

STRONGLY PRIME IDEAL

DIVIDED IDEAL

VALUATION DOMAIN

Abstract

Let R be a commutative integral domain with quotient field K and let P be a nonzero STRONGLY PRIME IDEAL of R. We give several characterizations of such ideals. It is shown that (P : P) is a VALUATION DOMAIN with the unique maximal ideal P. We also study when P-1 is a ring. In fact, it is proved that P-1 = (P : P) if and only if P is not invertible. Furthermore, if P is invertible, then R = (P : P) and P is a principal ideal of R.

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APA: Copy

JAHANINEZHAD, R.. (2010). THE DUAL OF A STRONGLY PRIME IDEAL. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 5(1), 19-26. SID. https://sid.ir/paper/310288/en

Vancouver: Copy

JAHANINEZHAD R.. THE DUAL OF A STRONGLY PRIME IDEAL. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2010;5(1):19-26. Available from: https://sid.ir/paper/310288/en

IEEE: Copy

R. JAHANINEZHAD, “THE DUAL OF A STRONGLY PRIME IDEAL,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 5, no. 1, pp. 19–26, 2010, [Online]. Available: https://sid.ir/paper/310288/en

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