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We derive an adjunction inequality for any smooth, closed, connected, oriented 4‐manifold   X   withb  +   =  1   . This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case ofb  1   =  0   . We demonstrate that the inequality is especially powerful when    2   χ  ˜   +  3  σ  ⩾  0   , where    χ  ˜    is the modified Euler number taking account of the cup product onH  1    (  X  ;  Z  )    .

Minimal genus for 4‐manifolds with b + = 1