Component of the 20S core proteasome complex involved in the proteolytic degradation of most intracellular proteins. This complex plays numerous essential roles within the cell by associating with different regulatory particles. Associated with two 19S regulatory particles, forms the 26S proteasome and thus participates in the ATP-dependent degradation of ubiquitinated proteins. The 26S proteasome plays a key role in the maintenance of protein homeostasis by removing misfolded or damaged proteins that could impair cellular functions, and by removing proteins whose functions are no longer required. Associated with the PA200 or PA28, the 20S proteasome mediates ubiquitin-independent protein degradation. This type of proteolysis is required in several pathways including spermatogenesis (20S-PA200 complex) or generation of a subset of MHC class I-presented antigenic peptides (20S-PA28 complex). The 26S proteasome consists of a 20S proteasome core and two 19S regulatory subunits. The 20S proteasome core is a barrel-shaped complex made of 28 subunits that are arranged in four stacked rings. The two outer rings are each formed by seven alpha subunits, and the two inner rings are formed by seven beta subunits. The proteolytic activity is exerted by three beta-subunits PSMB5, PSMB6 and PSMB7 (PubMed:12015144). Interacts with NOTCH3 (By similarity). Interacts with ZFAND1 (By similarity). Translocated from the cytoplasm into the nucleus following interaction with AKIRIN2, which bridges the proteasome with the nuclear import receptor IPO9. Belongs to the peptidase T1A family.