A higher level shared cache of a hierarchical cache of a multi-processor system utilizes transaction identifiers to manage memory conflicts in corresponding transactions. The higher level cache is shared with two or more processors. A processor may have a corresponding accelerator that performs operations on behalf of the processor. Transaction indicators are set in the higher level cache corresponding to the cache lines being accessed. The transaction aborts if a memory conflict with the transaction's cache lines from another transaction is detected, and the corresponding cache lines are invalidated. For a successfully completing transaction, the corresponding cache lines are committed and the data from store operations is stored.