Prime spectrum and primitive Leavitt path algebras G. Aranda PinoE. PardoM. Siles Molina 16D70Leavitt path algebrasprime idealmaximal tailprimitive ring In this paper a bijection between the set of prime ideals of a Leavitt path algebra $L_K(E)$ and a certain set which involves maximal tails in $E$ and the prime spectrum of $K[x,x^{-1}]$ is established. Necessary and sufficient conditions on the graph $E$ so that the Leavitt path algebra $L_K(E)$ is primitive are also found. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3516 10.1512/iumj.2009.58.3516 en Indiana Univ. Math. J. 58 (2009) 869 - 890 state-of-the-art mathematics http://iumj.org/access/