<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE ArticleSet PUBLIC "-//NLM//DTD PubMed 2.6//EN" "http://www.ncbi.nlm.nih.gov/corehtml/query/static/PubMed.dtd">
<ArticleSet>
<Article>
<Journal>
				<PublisherName>Iranian Mathematical Society (IMS)</PublisherName>
				<JournalTitle>Bulletin of the Iranian Mathematical Society</JournalTitle>
				<Issn>1017-060X</Issn>
				<Volume>37</Volume>
				<Issue>No. 3</Issue>
				<PubDate PubStatus="epublish">
					<Year>2011</Year>
					<Month>09</Month>
					<Day>15</Day>
				</PubDate>
			</Journal>
<ArticleTitle>Second symmetric powers of  chain complexes</ArticleTitle><FirstPage>39</FirstPage>
			<LastPage>75</LastPage>
			<Language>en</Language>
<AuthorList>
<Author>
					<FirstName>A. J.</FirstName>
					<LastName>Frankild</LastName>
					<Affiliation></Affiliation>
				</Author>
<Author>
					<FirstName>S. </FirstName>
					<LastName>Sather-Wagstaff</LastName>
					<Affiliation></Affiliation>
				</Author>
<Author>
					<FirstName>A. </FirstName>
					<LastName>Taylor</LastName>
					<Affiliation></Affiliation>
				</Author>
</AuthorList>
			<History>
				<PubDate PubStatus="received">
					<Year>2009</Year>
					<Month>03</Month>
					<Day>30</Day>
				</PubDate>
			</History>
		<Abstract><![CDATA[We investigate Buchbaum and Eisenbud's construction of the second
symmetric power $s_R(X)$ of a chain complex $X$ of modules over
a commutative ring $R$. We state and prove a number of results
from the folklore of the subject for which we know of no good
direct references. We also provide several explicit computations
and examples. We use this construction to prove the following
version of a result of Avramov, Buchweitz, and c{S}ega: let
$Rto S$ be a module-finite ring homomorphism such that $R$ is
noetherian and local, and such that 2  is a unit in $R$. Let $X$
be a complex of finite rank free $S$-modules such that $X_n=0$
for each $n]]></Abstract>
		<ObjectList>
			<Object Type="keyword">
			<Param Name="value">Chain complex</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">symmetric power</Param>
			</Object>
			<Object Type="keyword">
			<Param Name="value">symmetric square</Param>
			</Object>
		</ObjectList>
</Article>
</ArticleSet>