Let R be a ring and let J(R), C(R) be its Jacobson radical and center, correspondingly. If R is a centrally essential ring and the factor ring R/J(R) is commutative, then any minimal right ideal is contained in the center C(R). A right Artinian (or right Noetherian subdirectly indecomposable) centrally essential ring is a right and left Artinian local ring. We describe centrally essential Noetherian subdirectly indecomposable rings and centrally essential rings with subdirectly indecomposable center. We give examples of non-commutative subdirectly indecomposable, centrally essential rings.

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