1. A computer program product for implementing a multithreaded transaction, the computer program product comprising: a computer readable storage medium having program instructions embodied therewith, the program instructions readable by a processing circuit to cause the processing circuit to perform a method comprising: assigning a same transaction identifier (ID) corresponding to the multithreaded transaction to a plurality of threads of the multithreaded transaction, wherein the plurality of threads execute the multithreaded transaction in parallel; determining one or more memory areas that are owned by the multithreaded transaction; receiving a memory access request from a requester that is directed to a memory area that is owned by the transaction; and based on determining that the requester has a transaction ID that matches the transaction ID of the multithreaded transaction, performing the memory access request without aborting the multithreaded transaction, wherein a number of the plurality of threads of the multithreaded transaction is specified by a TBEGIN instruction of the multithreaded transaction.