In this paper we begin a classification of simple and semisimple totally antiflexible algebras (finite-dimensional) over splitting fields of char.
≠
2
,
3
\ne 2,3
. For such an algebra
A
A
, let
P
P
be the largest associative ideal in
A
+
{A^ + }
and let
N
+
{N^ + }
be the radical of
P
P
. We determine all simple and semisimple totally antiflexible algebras in which
N
⋅
N
=
0
N \cdot N = 0
. Defining
A
A
to be of type
(
m
,
n
)
(m,n)
if
N
+
{N^ + }
is nilpotent of class
m
m
with
dim
A
=
n
\dim A = n
, we then characterize all simple nodal totally anti-flexible algebras (over fields of char.
≠
2
,
3
\ne 2,3
) of types
(
n
,
n
)
(n,n)
and
(
n
−
1
,
n
)
(n - 1,n)
and give preliminary results for certain other types.