ringen
to wrestle
To practice a combat sport in which two opponents try to force each other to the ground using strength and technique.
Die beiden Athleten rangen fair um den Meistertitel.
The two athletes wrestled fairly for the championship title.

to wrestle / struggle
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to wrestle
To practice a combat sport in which two opponents try to force each other to the ground using strength and technique.
Die beiden Athleten rangen fair um den Meistertitel.
The two athletes wrestled fairly for the championship title.

The meaning of 'ringen' (to wrestle / struggle) changes completely depending on the preposition used. Pay close attention to whether the verb stands alone or is combined with 'um' (for), 'mit' (with), or 'nach' (for/after).
Die Kinder rangen zum Spaß auf der Wiese.
The children wrestled for fun in the meadow.
Without a preposition or with a direct opponent ('ringen gegen jemanden' — to wrestle against someone), 'ringen' almost always describes the combat sport of the same name. The context here is usually athletic.
Schon als Kind hat er im Verein gerungen.
He already wrestled in a club as a child.
The expression 'ringen um' (to fight for) expresses an intense struggle for a goal. Typical goals are 'das Leben' (life), 'eine Lösung' (a solution), 'Anerkennung' (recognition), or 'die Macht' (power).
Die Firma ringt um ihr wirtschaftliches Überleben.
The company is fighting for its economic survival.
With the preposition 'mit' (with), 'ringen' describes an inner or difficult struggle. You can wrestle with 'mit sich selbst' (with oneself), 'mit einer Entscheidung' (with a decision), 'mit den Tränen' (with tears), or 'mit dem Schlaf' (with sleep).
Sie rang sichtlich mit den Tränen, als sie die traurige Nachricht hörte.
She was visibly fighting back tears when she heard the sad news.
The construction 'ringen nach' (to struggle for) describes a desperate, often physical search. It is almost always used in the fixed expressions 'nach Luft ringen' (to gasp for air), 'nach Worten ringen' (to struggle for words), or 'nach Fassung ringen' (to struggle to regain one's composure).
Nach dem langen Sprint rang der Läufer nach Luft.
After the long sprint, the runner gasped for air.
to search / look for
'suchen' and 'ringen' can both express that someone is making a strong effort to obtain or achieve something. 'suchen' is more neutral: you are trying to find a solution, an answer, or something concrete. 'ringen' sounds stronger and more difficult. It fits when there is effort, struggle, or inner pressure, for example with a decision or when someone is struggling for words. Learners may confuse the words because both show effort. As a guide: 'suchen' fits ordinary wanting-to-find, while 'ringen' is for a difficult struggle for something or with oneself.

Nach der schlechten Nachricht rang Maria lange um die richtigen Worte.
After the bad news, Maria struggled for a long time to find the right words.
Nach dem Fehler im Bericht sucht das Team gemeinsam nach einer Lösung.
After the mistake in the report, the team is searching for a solution together.