Was the Summarian civilization exclusively male dominated

no there was one queen listed in the the Sumerian king list. her name was Kubaba

The house of Kubaba" is mentioned "in the reign of Puzur-Nirah, king of Akšak" (line 38) in the Weidner "Chronicle", a propagandistic letter attempting to predate the shrine of Marduk to an early period: "Kubaba gave bread to the fisherman and gave water, she made him offer the fish to Esagila" (line 43). Her reign as the only "king" of the 3rd Dynasty of Kish was one of peace and prosperity. Her reign is contemporary with the "Early Dynastic III" period of Sumer. Her reign is listed to have lasted for 100 years. If she is a historical ruler, she probably lived in the 23rd to 25th century BC. Shrines in her honour spread throughout Mesopotamia[1][2]. In the Hurrian area she may be identified with Kebat, or Hepat, one title of the Hurrian Mother Goddess Hannahannah (from Hurrian hannah, "mother"). Abdi-Kheba (= the servant of Kheba), was the palace mayor, ruling Jerusalem at the time of the Amarna Letters (1350 BCE).