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The phrase "a rigid division between" is correct and usable in written English.
It can be used to describe a clear and inflexible separation or distinction between two or more entities, concepts, or groups.
Example: "There is often a rigid division between work and personal life that can lead to stress and burnout."
Alternatives: "a strict separation between" or "a clear boundary between".
Exact(1)
"When I went to Copenhagen [in 2009] I engaged in 24 hours of diplomacy to salvage from a pretty chaotic process the basic principle that every country had to participate, that we couldn't have a rigid division between developed countries and developing countries when it came to solving this problem".
Similar(59)
They uphold a rigid division of labor: Mr. Goldberg is the starring pianist, and the music, complex but never cold, is by Mr. Klein, who sticks to Fender Rhodes keyboard throughout.
It is obvious, after all, that this classification of the practices must not be intended as a rigid division in clearly distinct categories.
Especially when the safety of students was of concern, the observers did not feel a rigid division was necessary and always put the safety of the children first.
In contrast to phenomenalism, a position in the theory of knowledge (epistemology) with which it is often confused, phenomenology which is not primarily an epistemological theory accepts neither the rigid division between appearance and reality nor the narrower view that phenomena are all that there is (sensations or permanent possibilities of sensations).
But the underlying principle (beside France's great number of fonctionnaires and their stringently meritocratic and bureaucratic orders) is France's rigid division between public and private on which the affaire of Dominique Strauss-Kahn turned the spotlight.
Mr. Barbera said, "So there is not the rigid division between genres that there once was and it is clearly time to recognize this in the programming of categories at film festivals".
And they say the teams of women, known as the Daughters of Iraq, play a crucial role in a country where rigid divisions between the sexes make it awkward, sometimes unthinkable, for male police officers to frisk women and girls in search of the telltale lump of a gun or an explosive belt.
They argue using politeness and tact, but also making a habit of positive things, of compliments, of small surprises, of doing a partner's chore, if you have a fairly rigid division of labor.
By the Achaemenian period there developed a more rigid division of society into four basic classes: priests, nobles, farmers/herdsmen, and artisans.
Beyond a rigid labour division of central versus peripheral activities, multinational trials can be considered as social organizations that involve human and non- human components with the ultimate goal of scientific production.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com