id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
xd07gq7038v	Sara B. Quinn	Algorithmic Complexity of Algebraic Structures	2008		.txt	text/plain	376	12	35	Another idea explored in the present work is that of comparing the complexity of the classification problem for various classes of structures, using the notion of a Turing computable embedding.oindent extbf{Definition}.A Turing computable embedding of $K$ into $K'$ is an operator $Phi = varphi_e$ such that egin{enumerate}item for each $mathcal{A}in K$, there exists $mathcal{B}in K'$ such that $varphi_e^{D(mathcal{A})} = chi{D(mathcal{B})}$, anditem if $mathcal{A},mathcal{A}'in K$ correspond, respectively, to $mathcal{B},mathcal{B}'in K'$, then $mathcal{A}congmathcal{A}'$ if and only if $mathcal{B}congmathcal{B}'$. end{enumerate}oindentThe ordering of classes of structures that arises from this embedding allows us to compare the complexity of the classification problem for those classes. In the present work, we give characterizations for the classes of structures that embed into the class of equivalence structures, as well as into the class of reduced Abelian $p$-groups of various lengths.	cache/xd07gq7038v.txt	txt/xd07gq7038v.txt