  When carbon is ignited off-centre in a CO core of a super-AGB star, its
burning in a convective shell tends to propagate to the centre. Whether the C
flame will actually be able to reach the centre depends on the efficiency of
extra mixing beneath the C convective shell. Whereas thermohaline mixing is too
inefficient to interfere with the C-flame propagation, convective boundary
mixing can prevent the C burning from reaching the centre. As a result, a
C-O-Ne white dwarf (WD) is formed, after the star has lost its envelope. Such a
"hybrid" WD has a small CO core surrounded by a thick ONe zone. In our 1D
stellar evolution computations, the hybrid WD is allowed to accrete C-rich
material, as if it were in a close binary system and accreted H-rich material
from its companion with a sufficiently high rate at which the accreted H would
be processed into He under stationary conditions, assuming that He could then
be transformed into C. When the mass of the accreting WD approaches the
Chandrasekhar limit, we find a series of convective Urca shell flashes
associated with high abundances of 23Na and 25Mg. They are followed by
off-centre C ignition leading to convection that occupies almost the entire
star. To model the Urca processes, we use the most recent well-resolved data
for their reaction and neutrino-energy loss rates. Because of the emphasized
uncertainty of the convective Urca process in our hybrid WD models of SN Ia
progenitors, we consider a number of their potentially possible alternative
instances for different mixing assumptions, all of which reach a phase of
explosive C ignition, either off or in the centre. Our hybrid SN Ia progenitor
models have much lower C to O abundance ratios at the moment of the explosive C
ignition than their pure CO counterparts, which may explain the observed
diversity of the SNe Ia.
