Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
rīvālĭtas, ātis, f. [rivalis, II. B.], rivalship, rivalry in love (cf. aemulatio, rivalry in gen.), Cic. Tusc. 4, 26, 56; between women, App. M. 10, p. 250, 16: rivalitatem non amat victoria, P. Syri Sent. 575 Rib.