Yo soy mujer = Soy una mujer = Soy mujer

Yes, it means the same. In spanish we tend to remove the pronoun in when it is the subject of the sentence, as it is implied thanks to the verb conjugation. In the example you give, if you say "soy", it is clear that the subject is "yo". Other examples: Soy mujer (yo). Soy español (yo). Fui a Barcelona (yo). Comes mucho (tú).