<?xml version="1.0" encoding="utf-8"?>
<journal>
  <journal_metadata lang="en">
    <full_title>Bulletin of the Australian Mathematical
    Society</full_title>
    <abbrev_title>Bull. Austral. Math. Soc.</abbrev_title>
    <issn media_type="online">0004-9727</issn>
    <coden>ALNBAB</coden>
  </journal_metadata>
  <journal_issue>
    <publication_date media_type="online">
      <year>2005</year>
    </publication_date>
    <journal_volume>
      <volume>72</volume>
    </journal_volume>
    <issue>2</issue>
    <doi_data>
      <doi>10.wxyz/CV72P2</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P2/</resource>
    </doi_data>
  </journal_issue>
  <journal_article publication_type="full_text">
    <titles>
      <title>On $C^{*}$-algebras with the approximate $n$-th root
      property</title>
    </titles>
    <contributors>
      <person_name sequence="first" contributor_role="author">A.
      Chigogidze</person_name>
      <person_name sequence="additional" contributor_role="author">
      A. Karasev</person_name>
      <person_name sequence="additional" contributor_role="author">
      K. Kawamura</person_name>
      <person_name sequence="additional" contributor_role="author">
      V. Valov</person_name>
    </contributors>
    <publication_date media_type="online">
      <given_date>14 February 2006</given_date>
      <year>2006</year>
      <month>2</month>
      <day>14</day>
    </publication_date>
    <pages>
      <first_page>197</first_page>
      <last_page>212</last_page>
    </pages>
    <publisher_item>
      <item_number>722-5072-ChKaKaVa-2005</item_number>
    </publisher_item>
    <doi_data>
      <doi>10.wxyz/C2005V72P2p197</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P2/722-5072-ChKaKaVa/</resource>
    </doi_data>
    <extra_info>
      <abstract>We say that a $C^*$-algebra $X$ has the approximate
      $n$-th root property ($n\geq 2$) if for every $a\in X$ with
      $\|a\|\leq 1$ and every $\varepsilon &gt; 0$ there exists
      $b\in X$ such that $\|b\|\leq 1$ and $\|a-b^n\| &lt;
      \varepsilon $. Some properties of commutative and
      non-commutative $C^*$-algebras having the approximate $n$-th
      root property are investigated. In particular, it is shown
      that there exists a non-commutative (respectively,
      commutative) separable unital \break $C^*$-algebra $X$ such
      that any other (commutative) separable unital $C^*$-algebra
      is a quotient of $X$. Also we illustrate a commutative
      $C^*$-algebra, each element of which has a square root such
      that its maximal ideal space has infinitely generated first
      {\v C}ech cohomology.</abstract>
      <subject_class>46L85, 54C40</subject_class>
      <review type="MathReviews">MR2183403</review>
      <review type="Zentralblatt">02246384</review>
      <acknowledgement>The second author was partially supported by
      his NSERC Grant 257231-04. The paper was started during the
      third author's visit to Nipissing University in July 2004.
      The last author was partially supported by his NSERC Grant
      261914-03.</acknowledgement>
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