"basis of ideas" is a correct and usable phrase in written English.
It refers to the foundation or underlying principles on which a group of ideas or concepts is built. Example: The scientist's research was groundbreaking, as it challenged the very basis of ideas in the field of physics.
It is not likely that they won it on the basis of ideas.
Buddhism was not a completely new phenomenon in the religious history of India; it was built upon the basis of ideas that were already current, both Brahmanic and non-Brahmanic.
Not for nothing did he think of himself as "running for President" — a President's greatness depends, first of all, on winning an election in the world's biggest popularity contest, before winning the esteem of the élite on the basis of ideas and actions.
Life demands that we act, by choosing among competing goods on the basis of ideas that are often less than clear and distinct.
But, the products sometimes failed to satisfy the user requirements, because the products were designed on the basis of ideas and proprietary technologies of individual manufacturers.
The answer is unfortunately a resounding no: Vardanyan (1986) has proved on the basis of ideas by Artemov (1985) that the set of sentences of predicate provability logic all of whose realizations are provable in PA is not even recursively enumerable, so it has no reasonable axiomatization.
So many students of mine have become rich and famous on the basis of my ideas which pisses me off, because I'm not a nice person.
Yet there is a consistent failure on the part of local authorities and government reviews to grasp even the basis of the ideas that can underlie a different kind of education.
By abrogating the original agreement and moving forward with the plan anyway on the basis of the ideas Mr Veitch gave, Virgin is guilty of theft, the suit argues.
While scholars have often preferred the authority of Condivi, Vasari's lively writing, the importance of his book as a whole, and its frequent reprinting in many languages have made it the most usual basis of popular ideas on Michelangelo and other Renaissance artists.
(1.4) On the basis of the ideas exploited by [6], we derive some new oscillation results for (1.1).
