| Authors | فاطمه موذن,رضا جهانی نژاد |
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| Journal | Indian Journal of Pure and Applied Mathematics |
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| IF | ثبت نشده |
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| Paper Type | Full Paper |
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| Published At | 2026-09-07 |
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| Journal Grade | Scientific - research |
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| Journal Type | Electronic |
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| Journal Country | Iran, Islamic Republic Of |
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| Journal Index | JCR ,SCOPUS |
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| Keywords | Annihilator ideal · Zero divisor · Center of ring · Nil radical · Noetherian ring |
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Abstract
In this article, we introduce a new class of ideals of rings which consists of central annihilator ideals and demonstrate
how to use such ideals in the general study of the structure of rings. We study rings in which the left (right)
annihilator of each element is in its center. In the following, we present the structure of these rings. We also prove
a version of Cohen’s Theorem in rings that have a nonzero central annihilator ideal. Next, we show that the theory
of primary decomposition of proper ideals in commutative Noetherian rings can be extended to a similar primary
decomposition of central annihilator ideals.
