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The phrase "a common idea that" is correct and usable in written English.
It can be used when introducing a widely held belief or notion that is generally accepted by a group or society.
Example: "There is a common idea that hard work leads to success, but many factors contribute to achieving one's goals."
Alternatives: "a widely held belief that" or "a prevalent notion that".
Exact(7)
The two parts are unified by a common idea, that of redemption through the power of love, a unity conveyed through shared musical themes.
There is a common idea that a living organism is a sort of fight against entropy: it keeps entropy locally low.
It reflects a common idea that science deals with physical objects of study like photons, cells, and atoms, rather than a way of acquiring knowledge, she adds.
There is a common idea that modern technology buffers us from the harsh forces of nature like big predators and the plagues of past – which often conveniently forgets about the toll infectious diseases and epidemics take in the third world, even with modern medicine.
It took all these years until Steve and I were eye-to-eye and shared a common idea that gave it birth.
At heart, these two young artists both of whom are having buzz-worthy solo shows in New York galleries right now—share a common idea: that to deal with our racist past and present, we need to see the world with empathy and care.
Similar(53)
This is an extreme version of a more common idea, that there exists such things as "informational genes" that should be understood as distinct from the "material genes" that are made of DNA and localized in space and time.
Another common idea that comes up in our conversations is that these growers, animal raisers and fishmongers are a small bulwark against the ever-rising tide of monocrops, corporate farming and the fast food nation.
A common idea is that memories are consolidated during sleep.
A common idea is that similar sequences should be searched with 'hard' matrices (created from less divergent sequences) and remote sequences should be searched with 'soft' matrices (built from more divergent sequences) [ 50].
These data sources were combined to summarize the common ideas that emerged across the FMEA sessions.
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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