Author:
Nabi M.,Ahanger S. A.,Bano S.,Shah A. H.
Abstract
AbstractWe show that for each $$n\ge 2\in {\mathbb {N}}$$
n
≥
2
∈
N
, the varieties $${\mathbb {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$
V
n
=
[
x
1
x
2
x
3
=
x
1
n
x
i
1
x
i
2
x
i
3
]
where i is any non-trivial permutation of $$\{1,2,3\}$$
{
1
,
2
,
3
}
are closed. Further, we show that for each $$n\in {\mathbb {N}}$$
n
∈
N
, the varieties $${\mathcal {V}}_{n}=[x_1x_2x_3=x_1^nx_{i_1}x_{i_2}x_{i_3}]$$
V
n
=
[
x
1
x
2
x
3
=
x
1
n
x
i
1
x
i
2
x
i
3
]
where i is any non-trivial permutation of $$\{1,2,3\}$$
{
1
,
2
,
3
}
other than the permutation (231) are closed.
Publisher
Springer Science and Business Media LLC
Reference11 articles.
1. Abbas, S.; Wajih, A.; Shah, A.H.: On dominions and varieties of bands. Asian Eur. J. Math. 14(8), 2150140 (2020)
2. Ahanger, S.A.; Shah, A.H.: Epimorphisms, dominions and varieties of bands. Semigroup Forum 100, 641–650 (2020)
3. Ahanger, S.A.; Nabi, M.; Shah, A.H.: Closed and saturated varieties of semigroups. Commun. Algebra (2022). https://doi.org/10.1080/00927872.2022.2095565
4. Alam, N.; Khan, N.M.: Epimorphisms, dominions and regular semigroups. J. Semigroup Theory Appl. 1, 34–45 (2012)
5. Alam, N.; Khan, N.M.: Special semigroup amalgams of quasi unitary subsemigroups and of quasi normal bands. Asian Eur. J. Math. 6(1), 1350010–7 (2013)