Here's a very basic approach:
sapply(strsplit(a, "\."), `[[`, 1)
# [1] "asdasd" "segssddfge" "se"
And another:
sub(".sss", "", a, fixed = TRUE)
# [1] "asdasd" "segssddfge" "se"
## OR sub("(.*)\..*", "\1", a)
## And possibly other variations
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