COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.

258 Takayuki Tamura
distinct (but not necessarily isomorphically distinct) direct products, i.e.
D = fi (S(Oi)XTi), m G 4,
i=l
where T = b . :
T,, T, s are right zero semigroups and either Bi = n(Ti)
1=1
(i= 1, . . . . m) or 0: = Z(Ti) (i = 1, . . ., m).
III. Right generalproduct of S by right zero semigroup.
First let T = {a, /3}, 0: a /I .
The equations (2.9’) are
tJ UP
e *u. a 95 e+ = e+ ++b e.,
e+ ag e., = e., +b e.,
8 *(L (I x e., = e., x0 e.,
e., a+k e+ = e., ++c, e+ 1
A relation w is defined on Gs as follows:
8 x 7 if and only if
Recall that
Using these notations,
fu7== h7
b+d3== he
zy: = zex, zy: = xez.
for all a E S.
(2.14)
Therefore x -, 1ys? is an anti-homomorphism of a semigroup S(0) into the
left regular representation of a semigroup S(q).
We have obtained all non-isomorphic right general products of S,
ISI =z 3, by a right zero semigroup of order 2. The results will be published
elsewhere.
IV. General product of S bq’ a right zero semigroup T of order 2.
aB
LetT={a,/3}, a a/3.
B aB
- -
e.
1
- -
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
.-
662, 6,
_.
_.
I
1
Semigroups and groupoids
TABLE 9+
4 - 7
rl
2, 3, 3,, 8, 8’, 9, 9,, 10, lo,, 13, 13,, 14, 14,, 14’, 14;, 15, 15,. 17, 18, 18,
2, 3, 15
4, 52, 16
42, 5, 162
7, 71, 11, 12,
2, 8, 14’. 14;
2, 9, 18
2, 10, 10,
7, 71, 11
7*, 12
2, 13, 131, 17
2, 8’, 14, 14,
2, 3, 15
4, 52, 16
2, 13, 131, 17
2, 9, 18
I
t These were computed by P. Dubois, J. Youngs, T. Okamoto, R. Kaneiwa, and
A. Ohta under the author’s direction.
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