Can I be dismissed without proper notice?

Yes, you can. This can occur if your employer regards your dismissal as being for gross misconduct because, for example, you have breached an important rule, which, it is stated, could lead to dismissal without notice, or that your conduct has been so serious that it amounts to a fundamental breach of the contract of employment.

Such a dismissal is called a 'summary dismissal', but to remain fair, it should be handled with procedural fairness.

It may be lawful to pay wages in lieu of notice, but only if the contract of employment expressly provides for it, or the employee agrees to waive notice.