Peremptory, a.
Etymology: [L. peremptorius destructive, deadly, decisive, final: cf. F. péremptorie. See Perempt.]
1. Precluding debate or expostulation; not admitting of question or appeal; positive; absolute; decisive; conclusive; final. Think of heaven with hearty purposes and peremptory designs to get thither. Jer. Taylor.
2. Positive in opinion or judgment; decided; dictatorial; dogmatical. Be not too positive and peremptory. Bacon. Briefly, then, for we are peremptory. Shak.
3. Firmly determined; unawed. [Poetic] Shak. Peremptory challenge (Law) See under Challenge. -- Peremptory mandamus, a final and absolute mandamus. -- Peremptory plea, a plea by a defendant tending to impeach the plaintiff's right of action; a plea in bar.
Syn. -- Decisive; positive; absolute; authoritative; express; arbitrary; dogmatical.
Shades of meaning
Fernald has no entry of its own for peremptory; he lists it under absolute.
Where he writes about it:
Authoritative is used always in a good sense, implying the right to claim authority; imperative, peremptory, and positive are used ordinarily in the good sense; as, an authoritative definition; an imperative demand; a peremptory command; positive instructions; imperious signifies assuming and determined to command, rigorously requiring obedience. — from absolute