Cement admixture, cement composition and method for laying work the same, and method for producing cement hardened product

An admixture for cement comprising three components of a copolymer (A), an unsaturated (poly)alkylene glycol ether monomer (a) and a non-polymerizable (poly)alkylene glycol (B) having no alkenyl group at ratios of the unsaturated (poly)alkylene glycol ether monomer (a) to the copolymer (A) in a range of 1 to 100% by mass and the non-polymerizable (poly)alkylene glycol (B) having no alkenyl group to the copolymer (A) in a range of 1 to 50% by mass,

• wherein the copolymer (A) contains a constituent unit (I) derived from the unsaturated (poly)alkylene glycol ether monomer (a) and a constituent unit (II) derived from a maleic acid monomer (b) at ratios of the constituent unit (I) and the constituent unit (II) in a range of 1% by mass or more, respectively, in the entire constituent units,
• and the unsaturated (poly)alkylene glycol ether monomer (a) is represented by the general formula (1):
• YO(R1O)nR2 (1)
• wherein Y represents an alkenyl group containing 2 to 4 carbon atoms, R2 represents a hydrogen atom or a hydrocarbon group containing 1 to 30 carbon atoms, R1O represents one or more species of oxyalkylene groups containing 2 to 18 carbon atoms, and n represents the average molar number of addition of the oxyalkylene groups and is a number of 1 to 500.