Is Satan the corrupt angel Lucifer?
My answer NO. Way you may ask. Satan is not evil or corrupt in the first place(as I see it) unless God is. Satan is an Angel of God, and will be at lest in the eyes of the Jews were the being known as Satan first is seen.
In Judaism there is no concept of a devil like in mainstream Christianity or Islam. In Hebrew, the biblical word ha-satan (שָׂטָן
means "the adversary"[2] or the obstacle, or even "the prosecutor" (recognizing that God is viewed as the ultimate Judge).
In the book of Job (Iyov), ha-satan is the title, not the proper name, of an angel submitted to God; he is the divine court's chief prosecutor. In Judaism ha-satan does not make evil, rather points out to God the evil inclinations and actions of humankind. In essence ha-satan has no power unless humans do evil things. After God points out Job's piety, ha-satan asks for permission to test the faith of Job. The righteous man is afflicted with loss of family, property, and later, health, but he still stays faithful to God. At the conclusion of this book God appears as a whirlwind, explaining to all that divine justice is inscrutable. In the epilogue Job's possessions are restored and he has a second family to "replace" the one that died.
In the Torah, ha-satan is mentioned several times. The main time is during the incident of the golden calf. As the source of people's evil inclination, or yetser harah, he is responsible for the Israelites building the golden calf while Moses was on Mount Sinai receiving the Torah from God. In the book of Chronicles, ha-satan incites David to an unlawful census.
In fact, the Book of Isaiah, Job, Ecclesiastes, and Deuteronomy all have passages in which God is credited for creating both the good and the evil of this world.(wiki)
Where Satan does appear in the Bible as a member of God's court, he plays the role of the Accuser, much like a prosecuting attorney for God.
According to the article on 'Satan' in the Jewish Encyclopedia, Satan's role as the accuser is found
in the prologue to the Book of Job, where Satan appears, together with other celestial beings or 'sons of God,' before the Deity, replying to the inquiry of God as to whence he had come, with the words: 'From going to and fro in the earth, and from walking up and down in it.' (Job 1:7) Both question and answer, as well as the dialogue which follows, characterize Satan as that member of the divine council who watches over human activity, but with the evil purpose of searching out men's sins and appearing as their accuser. He is, therefore, the celestial prosecutor, lawyer who sees only iniquity; for he persists in his evil opinion of Job even after the man of Uz has passed successfully through his first trial by surrendering to the will of God, whereupon Satan demands another test through physical suffering. (ib. ii. 3-5.)
Yet it is also evident from the prologue that Satan has no power of independent action, but requires the permission of God, which he may not transgress. He cannot be regarded, therefore, as an opponent of the Deity; and the doctrine of monotheism is disturbed by his existence no more than by the presence of other beings before the face of God. This view is also retained in Zech. 3:1-2, where Satan is described as the adversary of the high priest Joshua, and of the people of God whose representative the hierarch is; and he there opposes the 'angel of the Lord' who bids him be silent in the name of God.
In both of these passages Satan is a mere accuser who acts only according to the permission of the Deity; but in I Chron. 21:1 he appears as one who is able to provoke David to destroy Israel. The Chronicler (third century B.C.) regards Satan as an independent agent, a view which is the more striking since the source whence he drew his account (II Sam. 24:1) speaks of God Himself as the one who moved David against the children of Israel. Since the older conception refers all events, whether good or bad, to God alone, (I Sam. 16:14; I Kings 22:22; Isa. 45:7; etc) it is possible that the Chronicler, and perhaps even Zechariah, were influenced by Zoroastrianism, even though in the case of the prophet Jewish monism strongly opposed Iranian dualism. (Stave, Einfluss des Parsismus auf das Judenthum, pp. 253 et seq.) An immediate influence of the Babylonian concept of the 'accuser, persecutor, and oppressor' (Schrader, K. A. T. 3d ed., p. 463) is impossible, since traces of such an influence, if it had existed, would have appeared in the earlier portions of the Bible."(wiki)
Now for Lucifer. From what I know Lucifer really doesn't have any roots in Christian, and the name doesn't show in Hebrew at all. But I have heard it was one of many names for a Roman God.
But in the end they can be anything you want them to be, and seen how you want. Depending on what I'm doing really depends at the time how I see them and what they mean it me.