What is the difference between "were" and "have been", and are these sentences gramatically correct?
1) some of the best known writers of detective fiction in the twentieth century were women.
2) some of the best known writers of detective fiction in the twentieth century have been women.
Keep in mind that a present perfect casts its predication in the present tense. It does not narrate past events, it mentions past events which give rise to a present state.
That is why formal English does not permit a present perfect to be used with a temporal adjunct which does not include the present moment, the Speech Time at which the sentence is uttered. (You will occasionally find this rule violated in improvised, conversational discourse; but even there it is comparatively rare.) Thus, this is acceptable:
okI have often visited London.
But this is not:
∗ I have often visited London in the 1990s.
Today, in the 20th century is a timeframe which excludes the present. Consequently:
Sentence 1) is acceptable if it appears in a text written in the present century, but would be of questionable acceptability if written fifteen years ago.
Sentence 2) is acceptable if it appeared in a text written during the 20th century, but it would not be acceptable if written today.
There is a great deal more about this at What is the perfect, and how should I use it?, especially §§ 3.1 Grammatical meaning, 3.2 Pragmatic meaning and 4. When and how should I use the perfect?.
∗ marks a usage as unacceptable
They are both grammatical, and have a roughly similar meaning.
The first is in the simple past tense, and refers to a situation of the past (i.e. definitely before the present moment) and without connection to the present (nothing is implied about what may be true now).
The second is the present perfect tense, which refers to a situation of the past but in an unspecified manner that may continue to the present moment. This form tends to be used for the recent past.
The fact that the sentence also specifies a particular time period that has passed tends to equalize the effective meaning.
Many native English speakers do not grasp these differences clearly, and in practice either could be used with little difference in style or meaning.
