On Soteriology

Let me start off by saying how salvation is obtained: by grace alone, through faith alone (Ephesians 2:8-9), in Christ alone (John 3:16, 36). Works cannot add on to saving faith, otherwise saving faith is no longer saving faith. Jesus told the repentant thief on the cross that he would be with Him in paradise that day (Luke 23:43) and I think this is a clear example of someone who had been saved but had little to no opportunity for good works because he had a "deathbed" conversion.

The question I pose is: what is the role of Christ-centered Lordship in the life of a human? Is there a such thing as a 'carnal Christian' i.e. someone who claims to trust Christ as his/her personal Savior, but whose life indicates no fruit of the Spirit, no evidence at all of submitting to His Lordship? Is it possible to have saving faith without repentance? Can someone be a convert without having a heartfelt commitment to discipleship (in other words, not that the person is perfect in sanctification, but that he/she desires to submit his/her life to Jesus Christ)?

Which equation do you think most accurately describes salvation? (I believe I got this from Essential Truths of the Christian Faith by R.C. Sproul)

Works = Salvation
Faith + Works = Salvation
Faith = Salvation
Faith = Salvation + Works

I know many of the likes of Ryrie and Macarthur have written extensively on this topic, but I was hoping to get your thoughts on the matter.........