Concerning a summary for Synge's Riders to the Sea, eNotes Question and Answer section is not really a place for lengthy summaries, if that's what you mean by "full text" summary. If you mean a summary of the "full text" of the play, I can give you a short summary of the play.
The play involves an Irish peasant family living on a barren island. The action opens with two sisters receiving evidence that might possibly have belonged to their brother who has been missing at sea for nine days. They temporarily hide the evidence from their mother, because they don't want to disturb their mother until they know for sure that it is their brother Michael's property.
The girls' other brother (Bartley) wants to go to sea, too. The matriarch of the family (Maurya) doesn't want him to to go. She has already lost her husband and other sons to the sea, and she doesn't want to lose the last one. In short, he goes anyway, but doesn't even make it down the trail to the sea. Maurya, trying to head him off in order to give him his forgotten lunch, sees Michael's ghost riding on the horse behind Bartley, and receives the news shortly thereafter (back at the cottage) that Bartley fell off of his horse into the sea and drowned.
The evidence turns out to, indeed, be Michael's, and now Bartley is dead, too. Maurya now finds a kind of terrible peace. She now has nothing left that the sea can take from her. She has nothing left to lose.
Of course, this summary does not in any way do the play justice. The text is full of Aran Island dialect, abounds in Greek and Irish mythology, and closes with an extremely poignant scene, and much more.
The play takes place on an island west of Ireland.
After Nine days of constant grieving for her missing son, Michael, old
Maurya is fallen into a restless sleep. Her daughter, Cathleen, is busy
with household tasks, when another daughter, Nora, slips quietly into
the kitchen with a bundle given her by the young priest. It contains
part of the clothes taken from the body of a drowned man far in the
north. They have been sent to the family for identification, since the
clothes may belong to her missing brother.
The girls go to open the package but then decide to hide it in case
their mother, who is waking up, should come in and see them crying.
Maurya enters. After the sea had claimed the lives of her husband
and four eldest sons, Maurya tries to discourage Bartley, her last
living son, from going to Connemara to sell a horse, which was the
trip Michael took when he died. But Bartley insists that he will cross
the mainland in spite of winds and high seas.
Mad and aggravated at Bartley for not listening to her pleas, Maurya
allows him to go, however, without her blessing. Cathleen and Nora
persuade their mother to chase Bartley with the food they forgot to
give him and to give him her blessing regardless of her fears. While
she is gone the girls open the package. Nora recognizes her own
stitching in one of the socks, and immediately knows that the owner
of the clothes was indeed her brother, Michael. Their only comfort is
the hope that his body has been given a good Christian burial where
it was washed up.
Maurya returns horrified with a vision she has seen of Michael riding
on the horse behind Bartley. She claims that the vision proves that
her fear of Bartley’s death is being realized. When her daughters
show Maurya the clothes her only response is that the boards she
bought for Michael’s coffin will serve for Bartley instead.
As Maurya speaks the neighboring women enter keening. The Men
follow shortly, carrying the body of Bartley who has been knocked off
a cliff into the waves by the horse he was intending to sell. The play
closes on the note of Maurya’s accepting surrender to the sea, and
to the course of life: “They’re all gone now and there isn’t anything
mire the sea can do to me… No man at all can be living forever and
we must be satisfied.”