query: $I$ is a separable closed ideal of $A$. Does $I$ always have sequential quasicentral approximate unit?
positive_passages.docid: 20919
positive_passages.text: A lemma about quasicentral-approximate-unit
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 144250
negative_passages.text: subideals of an ideal
negative_passages.docid: 28244
negative_passages.text: Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
negative_passages.docid: 93629
negative_passages.text: Ideal quotient of fractional ideals
negative_passages.docid: 53469
negative_passages.text: C(0, 1) has infinitely many prime ideals not of the form Mp
negative_passages.docid: 136872
negative_passages.text: Why uniform closure $\mathscr{B}$ of an algebra $\mathscr{A}$ of bounded complex functions is uniformly closed?
negative_passages.docid: 149136
negative_passages.text: On the height of an ideal
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 70320
negative_passages.text: Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 97621
negative_passages.text: Every separable Banach space is isomorphic to $\ell_1/A$ for some closed $A\subset \ell_1$
negative_passages.docid: 15137
negative_passages.text: Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
negative_passages.docid: 114193
negative_passages.text: On the absolute norm of an ideal