This is how it is spelled....
a·pol·o·gy(-pl-j)
n. pl. a·pol·o·gies
1. An acknowledgment expressing regret or asking pardon for a fault or offense.
2.
a. A formal justification or defense.
b. An explanation or excuse: "The consequence of those measures will be the best apology for my conduct" Daniel Defoe.
3. An inferior substitute: The sagging cot was a poor apology for a bed.
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Noun 1. apology - an expression of regret at having caused trouble for someone; "he wrote a letter of apology to the hostess"
acknowledgement, acknowledgment - a statement acknowledging something or someone; "she must have seen him but she gave no sign of acknowledgment"; "the preface contained an acknowledgment of those who had helped her