  Intergalactic type-Ia supernovae (SNe-Ia) have been discovered recently in
rich galaxy clusters, likely the descendants of an intergalactic stellar
population found in recent years through a variety of tracers. We estimate the
observational signatures of the associated SN remnants (SNRs) in the unusual
intracluster medium (ICM) environment. If SNe-Ia still have a circumstellar
medium (CSM) at the time of explosion, then their remnants are visible in the
optical for ~100-1000 years, with properties similar to young galactic SNRs. In
contrast with galactic SNRs, in which the ejecta from the explosion interacts
with the ISM, intracluster SNRs become undetectable in the optical once their
ejecta passes beyond the CSM and enters the hot and tenuous ICM. If SNe-Ia have
a CSM, there should be ~150 young SNRs in the Virgo cluster, with
L(H-alpha)~10^{35} erg/s and angular size ~0.1''. We investigate the
possibility that members of this SNR population may have recently been
detected, but incorrectly identified as intergalactic HII regions.
Alternatively, if optical intergalactic SNRs do not exist in Virgo, this will
be evidence that SNe-Ia are devoid of a CSM, with implications for progenitor
scenarios. Regardless of the presence of a CSM, about 10 older radio SNRs per
square degree should be detectable in Virgo, with fluxes of ~0.1 mJy at 1 GHz.
Their angular sizes, morphologies, and lack of optical association with distant
galaxies can distinguish them from the much more numerous background
population. Their detection would provide a measurement of the intracluster SN
rate. Observations toward the site of SN1980I, a possibly intergalactic Virgo
SN-Ia, can test the existence of a CSM by comparison to our early-time
predictions for intergalactic SNR development.
