What is the ideology of the cold war and it's relation to the breakdown of wartime alliances aftger ww2?

Answer 1

The idealogy goes beyong the communist vs capitalist struggle. The cold war was all about empire building with the threat of nuclear obliteration hanging over the heads of the players. The U.S. built it's empire in Western Europe through NATO and used these ties to stick their fingers in the Middle East(Israel and Saudi Arabia) and Asia(Korea, Vietnam). The Soviets made their pushes in Eastern Europe(Warsaw Pact) and in China, Afghanistan, and Cuba.
Keep in mind, the US and Russia were only allied in the fight against the Nazis. There was a race to Berlin because whoever got there first could gain the biggest piece of Germany during the occupation phase after WWII. The only good things to come out of the cold war for the US were new stronger alliances with Great Britain and Japan.

Answer 2

Are you asking this question yourself or is it your homework? For me it sounds like it is the latter.

The political ideology of the cold war was of course communism against capitalism.

Iin order for both sides to get stronger to counter balance one another, new alliances were made from each side and due to that many ww2 alliances were broken.