  AGB stars are not expected to be X-ray-emitters, yet a small fraction of
them, the so-called X-AGBs, show X-ray emission that can be attributed to
coronal activity of a companion or accretion onto it. By searching the recently
released eROSITA-DE eRASS1 source catalog, we aim to increase the sample of
known X-AGBs. So far, 36 X-AGBs have been reported, including 21 previous ROSAT
RASS, Chandra and XMM detections and 15 more eROSITA eRASS1 recent detections.
We cross-correlated the position of sources in the eROSITA-DE eRASS1 catalog
with those of AGB stars to find possible X-ray counterparts. We carefully
checked these by comparing X-ray and near-IR $K$ images, disregarding those
affected by optical loading, diffuse sources, or unreliable positional
associations. Seven high-confidence X-AGBs and another seven possible ones are
found. Accounting for previous X-ray detections, the sample of X-AGBs is
increased from 36 up to 47, of which eROSITA-DE has so far discovered 26 new
X-AGBs, more than doubling the number of known X-AGBs. This demonstrates
eROSITA's capability to detect X-AGBs despite the challenge posed by the
optical loading caused by their near-IR brightness. The eRASS1 X-AGBs tend to
have higher X-ray luminosity than previously detected X-AGBs, suggesting a bias
toward brighter sources. A comparison of the X-ray and far-UV luminosity of
X-AGBs with those of X-ray-emitter symbiotic stars (X-SySts) revealed an
overlap in the X-ray luminosity range $10^{29.5}<L_X$ (erg s$^{-1}$)
$<10^{33.0}$. The average higher X-ray luminosity of X-SySts AGBs ($\approx
10^{32}$ erg s$^{-1}$) can be interpreted as X-ray emission arising from a
boundary layer between an accretion disk and a white dwarf, whereas the average
lower X-ray luminosity ($\approx5\times10^{30}$ erg s$^{-1}$) of X-AGBs would
arise from an accretion disk around main-sequence or subgiant F-K companion
stars.
